Product Description

Eigenvectors of graph Laplacians have not, to date, been the subject of expository articles and thus they may seem a surprising topic for a book. The authors propose two motivations for this new LNM volume: (1) There are fascinating subtle differences between the properties of solutions of Schrödinger equations on manifolds on the one hand, and their discrete analogs on graphs. (2) “Geometric” properties of (cost) functions defined on the vertex sets of graphs are of practical interest for heuristic optimization algorithms. The observation that the cost functions of quite a few of the well-studied combinatorial optimization problems are eigenvectors of associated graph Laplacians has prompted the investigation of such eigenvectors.

The volume investigates the structure of eigenvectors and looks at the number of their sign graphs (“nodal domains”), Perron components, graphs with extremal properties with respect to eigenvectors. The Rayleigh quotient and rearrangement of graphs form the main methodology.

Product Description
Through examples of large complex graphs in realistic networks, research in graph theory has been forging ahead into exciting new directions. Graph theory has emerged as a primary tool for detecting numerous hidden structures in various information networks, including Internet graphs, social networks, biological networks, or, more generally, any graph representing relations in massive data sets. How will we explain from first principles the universal and ubiquitous coherence in the structure of these realistic but complex networks? In order to analyze these large sparse graphs, we use combinatorial, probabilistic, and spectral methods, as well as new and improved tools to analyze these networks. The examples of these networks have led us to focus on new, general, and powerful ways to look at graph theory. The book, based on lectures given at the CBMS Workshop on the Combinatorics of Large Sparse Graphs, presents new perspectives in graph theory and helps to contribute to a sound scientific foundation for our understanding of discrete networks that permeate this information age. ... Read more

Customer Reviews (3)

excellent work
I am new to graph theory, pursue it as a hobby, write test applications in C#/.NET while struggling to understand theory with pencil and paper. I am very interested in understanding both generalizations of Erdos-Renyi graphs and spectral theory, and this book together with what you might call Fan Chung's companion book Spectral Graph Theory are a great basis for learning the ropes. I particularly appreciate the authors taking the time and space to explain the broader picture and the intuitive implications of theorems, a welcome divergence from the common practice of theorem-proof-theorem-proof ad nauseum. I highly recommend this book as both enjoyable and exciting to read!

Says more for Linyaun Lu than Fan Chung?
The presence of large scale graphs in this set of lectures doesn't really remedy the lack of lower scale pattern matrices/ graphs? This book is better than the ten year earlier Spectral Graph Theory (CBMS Regional Conference Series in Mathematics, No. 92) by Fan Chung alone.
Both are dry and near the bone in exposition, but I wish I had bought this one instead of the former.
Since Fan Chung seems to have not learned or done a lot in the ten years between, I put the difference to the co-author.
It is a crying shame and I really feel bad for a genius like Fan Chung to be so dry and uninspired on such an important subject as this.
There is so much more involved in complex graph theory than the dry bones presented in these texts.
Don't approach this text with a faint heart or a lack of will.

A very interesting book
The book summarizes recent developments in random graph theory, in particular the scale-free networks and small world networks, but classical Erdos-Renyi model is also covered. Many chapters have interesting introductions giving a brief historical background on the presented topic, followed by a series of rigorous proofs. There are numerous examples which relate the presented results to the real world empirical data, giving the reader further motivation to go through the mathematics. This book is certainly a "must have" item to anyone interested in modern graph theory and recent developments in the discipline. ... Read more

Product Description
This is a new edition of the now classic text. The already extensive treatment given in the first edition has been heavily revised by the author. The addition of two new sections, numerous new results and 150 references means that this represents an up-to-date and comprehensive account of random graph theory. The theory estimates the number of graphs of a given degree that exhibit certain properties. It not only has numerous combinatorial applications, but also serves as a model for the probabilistic treatment of more complicated random structures. This book, written by an acknowledged expert in the field, can be used by mathematicians, computer scientists and electrical engineers, as well as people working in biomathematics. It is self contained, and with numerous exercises in each chapter, is ideal for advanced courses or self study. ... Read more

Customer Reviews (2)

Standard reference in the subject
And has a lot of material, but the organization leaves much to be desired, and standard results in the field are there but very difficult to find (for example, good luck finding the proof of the classical Erdos-Renyi theorem on connectivity threshold for random graphs. The canonical proof is about half a page, while the proof you can back out of Bollobas is maybe two chapters. The configuration model (which is actually due to the author) is actually very simple and explained well in papers by N. Wormald. It is a little painful to read about in this book. Perhaps the most widely used property of random graphs is that they have the expander property (another result of Erdos). This is also carefully hidden.

It is also a little painful for me to give a less than glowing review of this, since I really like Modern Graph Theory, and random graphs are pervasive in modern mathematics, so we really need a good book. This one is not bad, but...

Written by a Master in the Field
This is the second book by Dr. Bollobas that I have read, and it is clear, that Dr. Bollobas is a master in the field.
It is amazing, how few lines he needs to motivate the subject matter completely.
The gaps in the proofs were sometimes large for me, but then again, the audience he wishes to address are "research students and professional mathematicians", and I am only a hobby mathematician.

The only minus point are the large number of misprints: I counted over 130 of them, and this is not counting misprints like 'some' instead of 'same', etc. This is very annoying if one uses the book for self study.

(Unfortunaltely misprints seem Dr. Bollobas' problem: Also the other book I read: 'Modern Graph Theory' had more than its share)


... Read more

Product Description
Combinatorics deals with the enumeration, existence, analysis, and optimization of discrete structures. With this study guide, students can master this growing field--with applications in several physical and social sciences, including chemistry, computer science, operations research, and statistics. Includes hundreds of problems with detailed solutions. ... Read more

Customer Reviews (5)

Excellent Text Book
This is great textbook. Like all the Schaum Outlines, the focus is on problem solving. The author (Prof. V.K. Balakrishnan) does an absolutely marvelous job in leading the reader to an understanding of basic combinatorics via a seemingly endless series of problems. The problems are clearly stated and the solutions are well done. The general quality of the book is very high.
If you need more exposition, I would suggest something like Notes on Introductory Combinatorics by Polya, Tarjan and Woods, but as I say, I think the book by Balakrishnan is just fine as it is.

Not ideal "self-study" book for undergrads
The book does a poor job at laying out the basics for the reader. In the first chapter only 2 pages out of 33 are dedicated to describing the theory, the rest of the chapter consists of word problems. Some of those word problems go beyond the scope of the theory outlined for you, to which I thought was not only unfair but a bit intimidating to the curious math student. Sadly, the majority of this book follows the same routine.

From this layout it was clear that this book wasn't written with the complete novice in mind. The Discrete Math [also a Schaum's outline] book I bought alongside this one happens to cover the same topics and does a much better job at explaining the basics with reasonable problems to practice from.

As I said before, I can't recommend this book to anyone who is looking to break way into Combinatorics.

kind of good
Not bad for those that have become accustomed to extensive math language within a text. The underlying concepts are explained well, however the density of material does take something away. Graph and group theory explanations should be more comprehensive. Considering the complexity of the various topics being presented this book is kind of good.

Nice job
Combinatorics is an area of mathematics that is frequently looked on as one that is reserved for a small minority of mathematicians: die-hard individualists who shun the limelight and take on problems that most would find boring. In addition, it has been viewed as a part of mathematics that has not followed the trend toward axiomatization that has dominated mathematics in the last 150 years. It is however also a field that has taken on enormous importance in recent years do its applicability in network engineering, combinatorial optimization, coding theory, cryptography, integer programming, constraint satisfaction, and computational biology. In the study of toric varieties in algebraic geometry, combinatorics has had a tremendous influence. Indeed combinatorial constructions have helped give a wide variety of concrete examples of algebraic varieties in algebraic geometry, giving beginning students in this area much needed intuition and understanding.It is the the advent of the computer though that has had the greatest influence on combinatorics, and vice versa.The consideration of NP complete problems typically involves enumerative problems in graph theory, one example being the existance of a Hamiltonian cycle in a graph. The use of the computer as a tool for proof in combinatorics, such as the 4-color problem, is now legendary.In addition, several good software packages, such as GAP and Combinatorica, have recently appeared that are explicitly designed to do combinatorics. One fact that is most interesting to me about combinatorics is that it gave the first explicit example of a mathematical statement that is unprovable in Peano arithmetic. Before coming across this, I used to think the unprovable statements of Godel had no direct relevance for mathematics, but were only interesting from the standpoint of its foundations.

This book is an introduction to combinatorics for the undergraduate mathematics student and for those working in applications of combinatorics. As with all the other guides in the Schaums series on mathematics, this one has a plethora of many interesting examples and serves its purpose well. Readers who need a more in-depth view can move on to more advanced works after reading this one. The author dedicates this book to the famous mathematician Paul Erdos, who is considered the father of modern combinatorics, and is considered one of most prolific of modern mathematicians, with over 1500 papers to his credit.

The author defines combinatorics as the branch of mathematics that attempts to answer enumeration questions without considering all possible cases. The latter is possible by the use of two fundamental rules, namely the sum rule and the product rule. The practical implementation of these rules involves the determination of permutations and combinations, which are discussed in the first chapter, along with the famous pigeonhole principle. Most of this chapter can be read by someone with a background in a typical college algebra course. The author considers some interesting problems in the "Solved Problems" section, for example one- and two-dimensional binomial random walks, and problems dealing with Ramsey, Catalan, and Stirling numbers. The consideration of Ramsey numbers will lead the reader to several very difficult open problems in combinatorics involving their explicit values.

Generalized permutations and combinations are considered in chapter two, along with selections and the inclusion-exclusion principle. The author proves the Sieve formula and the Phillip Hall Marriage Theorem. In the "Solved Problems" section, the duality principle of distribution, familiar from integer programming is proved, and the author works several problems in combinatorial number theory. A reader working in the field of dynamical systems will appreciate the discussion of the Moebius function in this section. Particularly interesting in this section is the discussion on rook and hit polynomials.

The consideration of generating functions and recurrence relations dominates chapter 3, wherein the author considers the partition problem for positive integers. The first and second identities of Euler are proved in the "Solved Problems" section, and Bernoulli numbers, so important in physics, are discussed in terms of their exponential generating functions. The physicist reader working in statistical physics will appreciate the discussion on Vandermonde determinants. Applications to group theory appear in the discussion on the Young tableaux, preparing the reader for the next chapter.

A more detailed discussion of group theory in combinatorics is given in chapter 4, the last chapter of the book. The author proves the Burnside-Frobenius, the Polya enumeration theorems, and Cayley's theorem in the "Solved Problems" section. Readers without a background in group theory can still read this chapter since the author reviews in detail the basic constructions in group theory, both in the main text and in the "Solved Problems" section. Combinatorial techniques had a large role to play in the problem of the classification of finite simple groups, the eventual classification proof taking over 15,000 journal pages and involving a large collaboration of mathematicians. Combinatorics also made its presence known in the work of Richard Borchers on the "monstrous moonshine" that brought together ideas from mathematical physics and the largest simple group, called the monster simple group.

The author devotes an appendix to graph theory, which is good considering the enormous power of combinatorics to problems in graph theory and computational geometry. Even though the discussion is brief, he does a good job of summarizing the main results, including a graph-theoretic version of Dilworth's theorem. Combinatorial/graph-theoretic considerations are extremely important in network routing design and many of the techniques discussed in this appendix find their way into these kinds of applications. The author asks the reader to prove that Dilworths' theorem, the Ford-Fulkerson theorem, Hall's marriage theorem, Konig's theorem, and Menger's theorem are equivalent. A very useful glossary of the important definitions and concepts used in the book is inserted at the end of the book.

excellent book !
In its usual way schaum's series gives out another book which is both helpful yet concise. This book gives the essential grounding for combinatorics and graph theory without being overly gargantuan encyclopedia..ample problems set the tone for a future mathematician. theycould've done better though..hence not the perfect 5 ! ... Read more

Product Description
Clear, comprehensive introduction emphasizes graph imbedding but also covers thoroughly the connections between topological graph theory and other areas of mathematics. Discussion of imbeddings into surfaces is combined with a complete proof of the classification of closed surfaces. Authors explore the role of voltage graphs in the derivation of genus formulas, explain the Ringel-Youngs theorem—a proof that revolutionized the field of graph theory—and examine the genus of a group, including imbeddings of Cayley graphs. 1987 edition. Many figures.
... Read more

Customer Reviews (2)

A recognized Classical text
This book had much that I needed to know about graph theory.
It is well written and includes much of the information needed.

It has three problems in notation that bother me:
1) Bn for Bouquets is like the Bn used for Braid groups.
2) definitions of "stars" are more the classical star than
the current usage as central point with radial connections.
3)The book doesn't distinguish well enough
between "graphs" with are symmetrical adjacency matrices
and "digraphs" and ends up confusing the issue it should clarify.

The book also shorts the reader on matrix theory connected to the graphs.
It tends to use an older approach to graphs that has to be adapted to modern computer mathematical systems.

Excellent
This book is written at a graduate level.It is written, for the most part, clearly and methodically.There are about 300 problems throughout the text, but there are no solutions in this book for those problems.

Titles of the 6 Chapters (with the number of pages in each chapter): 1) Introduction (to graph theory), 55; 2) Voltage Graphs and Covering Spaces, 40; 3) Surfaces and Graph Embeddings, 68; 4) Imbedded Voltage Graphs and Current Graphs, 54; 5) Map Colorings, 35; and 6) The Genus of a Group, 71.

This book is sufficient for self-study. ... Read more

Product Description
Designed as the bridge to cross the widening gap between mathematics and computer science, and planned as the mathematical base for computer science students, this maths text is written for upper-level college students who have had previous coursework involving proofs and proof techniques. The close tie between the theoretical and algorithmic aspects of graph theory, and graphs that lend themselves naturally as models in computer science, results in a need for efficient algorithims to solve any large scale problems. Each algorithm in the text includes explanatory statements that clarify individual steps, a worst-case complexity analysis, and algorithmic correctness proofs. As a result, the student will develop an understanding of the concept of an efficient algorithm. ... Read more

Customer Reviews (3)

Muy buen libro
Este libro me parece una referencia obligada para introducirse al tema de los algoritmos en gráficas. Las explicaciones son bastante claras e incluye numerosos ejercicios para practicar la teoría.

Bad, Bad Book
The book covers alot of topics in a very short amount of space. Too few examples, and several topics given only a few sentences.

Look elsewhere or get another book tosupplement it.

Excellent Reference on Graph Theory and Alorithm
This book covers topics ranging from NP completeness to introductory topics on graph theory and various algorithms on SPST, MST, etc. ... Read more

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The authors help you "see the math" through their focus on functions; visual emphasis; side-by-side algebraic and graphical solutions; real-data applications; and examples and exercises. By remaining focused on your needs, the authors will lead you to mathematical understanding and, ultimately, success in class.

Customer Reviews (2)

Math Class Books
College Algebra: Graphs and Models with Graphing Calculator Manual Package (4th Edition)
This is a great book.It walks you through step by step.All the vocaulary and formulas and important items are highlighted. Awesome book!

Not reliable
I paid for student copy but, he shipped me an instructor copy making it difficult to resell ... Read more

Product Description
This is the first book on the subject since itsintroduction more than fifty years ago, and it can be used as agraduate text or as a reference work. It features all of the keyresults, many very useful tables, and a large number of researchproblems. The book will be of interest to those interested in one ofthe most fascinating areas of discrete mathematics, connected tostatistics and coding theory, with applications to computer scienceand cryptography. It will be useful for anyone who is runningexperiments, whether in a chemistry lab or a manufacturing plant(trying to make those alloys stronger), or in agricultural or medicalresearch. Sam Hedayat is Professor of Statistics and Senior Scholar inthe Department of Mathematics, Statistics, and Computer Science,University of Illinois, Chicago. Neil J.A. Sloane is with AT&T BellLabs (now AT&T Labs). John Stufken is Professor Statistics at IowaState University. ... Read more

Customer Reviews (3)

book totally dedicated to orthogonal arrays
This book is a great collaboration. Hedayat is a statistician who has been a major developer of orthogonal arrays for statistical experimental designs, Stufken was a student of Hedayat who has worked with him on this research. Sloane comes from the mathematics of codign theory where he has developed orthogonal arrays to produce error correcting codes.
Orthogonal arrays were introduced by C. R. Rao in the 1940s. He developed them for applications to experiments. He also produced the seminal work and some important inequalities constraints for such arrays. Rao provides a great endorsement for this book in the forward he writes.

Many statistical texts on experimental designs include orthogonal arrays. Some books on coding theory include them also. However this is the first book entirely dedicated to orhtogonal arrays and their properties. Thus are married the major and diverse areas of applications. Orthogonal arrays are also of interest to mathematicians who work in abstract algebra because of the connection between the orthogonal arrays and Galois fields.

The authors provide an historical account of the field, the many applications including the revival in the 1980s through the robust designs of Taguchi whose fractional factorial experiments were all orthogonal designs.

The authors presentation is clear. They provide a clear definition of orthogonal arrays and give a thorough and up-to-date account of the literature. The text contains over 650 references. This is a must have book for anyone specializing in coding theory or the construction of efficient statistical designs.

Excellent..except for.....
The three authors have done a superb job of conveying their message. However, I feel that the book is a little over-drawn and long. It is still an excellent example of the supreme books that Springer releases.Congratulations to this BRILLIANT trio!

A Trio to die for.
Stufken and Hedayat have put together a book that is beyond words. It isone of the few textbooks dealing with Orthogonal Arrays that I've been ableto fully understand. Congratulations Stufken and Hedayat ... Read more

Product Description
This book combines traditional graph theory with the matroid view of graphs in order to throw light on the mathematical approach to network analysis. The authors examine in detail two dual structures associated with a graph, namely circuits and cutsets. These are strongly dependent on one another and together constitute a third, hybrid, vertex-independent structure called a graphoid, whose study is here termed hybrid graph theory. This approach has particular relevance for network analysis. The first account of the subject in book form, the text includes many new results as well as the synthesizing and reworking of much research done over the past thirty years (historically, the study of hybrid aspects of graphs owes much to the foundational work of Japanese researchers). This work will be regarded as the definitive account of the subject, suitable for all working in theoretical network analysis: mathematicians, computer scientists or electrical engineers. ... Read more

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This book, suitable for graduate students and professional mathematicians alike, didactically introduces methodologies due to Furstenberg and others for attacking problems in chromatic and density Ramsey theory via recurrence in topological dynamics and ergodic theory, respectively. Many standard results are proved, including the classical theorems of van der Waerden, Hindman, and Szemerdi. More importantly, the presentation strives to reflect the extent to which the field has been streamlined since breaking onto the scene around twenty years ago. Potential readers who were previously intrigued by the subject matter but found it daunting may want to give a second look. ... Read more

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Beginning with the origin of the four color problem in 1852, the field of graph colorings has developed into one of the most popular areas of graph theory. Introducing graph theory with a coloring theme, Chromatic Graph Theory explores connections between major topics in graph theory and graph colorings as well as emerging topics.

This self-contained book first presents various fundamentals of graph theory that lie outside of graph colorings, including basic terminology and results, trees and connectivity, Eulerian and Hamiltonian graphs, matchings and factorizations, and graph embeddings. The remainder of the text deals exclusively with graph colorings. It covers vertex colorings and bounds for the chromatic number, vertex colorings of graphs embedded on surfaces, and a variety of restricted vertex colorings. The authors also describe edge colorings, monochromatic and rainbow edge colorings, complete vertex colorings, several distinguishing vertex and edge colorings, and many distance-related vertex colorings.

With historical, applied, and algorithmic discussions, this text offers a solid introduction to one of the most popular areas of graph theory.

Product Description
The theory of random graphs began in the late 1950s in several papers by Erdos and Renyi. In the late twentieth century, the notion of six degrees of separation, meaning that any two people on the planet can be connected by a short chain of people who know each other, inspired Strogatz andWatts to define the small world random graph in which each site is connected to k close neighbors, but also has long-range connections. At about the same time, it was observed in human social and sexual networks and on the Internet that the number of neighbors of an individual or computer has a power law distribution. This inspired Barabasi and Albert to define the preferential attachment model, which has these properties. These two papers have led to an explosion of research. While this literature is extensive, many of the papers are based on simulations and nonrigorous arguments. The purpose of this book is to use a wide variety of mathematical argument to obtain insights into the properties of these graphs. A unique feature of this book is the interest in the dynamics of process taking place on the graph in addition to their geometric properties, such as connectedness and diameter. ... Read more

Customer Reviews (1)

Good text for technical readers
The author presents very interesting material and I really learned a lot from reading this book. I've read a lot of texts and papers on the subject of random graphs (both technical and for the general public) and most authors do a good job in making this subject interesting and enjoyable, but often lack a rigorous presentation of the subject. In that sense Durrett's book does an excellent job in providing this missing element from other books. On the negative side, the exposition in Durrett' sbook is not self-contained and the author relies too much on the notation and results from his previously published books.If you don't have those books the reading pace will be seriously hampered.Also, in trying to motivate the subject in Chapter 1, the author introduces a lot of cryptic notation and concepts that are not explained until later on. I know this is supposed to be a monograph, but at least the author should try to live up to the series mission of providing a clear presentation of the subjects. In summary, a great book if you are already familiar with the subject and are fairly mathematical sophisticated, but don't use this book as an introductory text or to get motivation on the subject. ... Read more

Product Description
This book introduces graph theory, a subject with a wide range of applications in real-work situations. This book is designed to be easily accessible to the novice, assuming no more than a good grasp of algebra to understand and relate to the concepts presented. Using many examples, illustrations, and figures, it provides an excellent foundation for the basic knowledge of graphs and their applications.This book includes an introductory chapter that reviews the tools necessary to understand the concepts of graphs, and then goes on to cover such topics as trees and bipartite graphs, distance and connectivity, Eulerian and Hamiltonian graphs, graph coloring, matrices, algorithms, planar graphs, and digraphs and networks.Graph theory has a wide range of applications; this book is useful for those in the fields of anthropology, computer science, chemistry, environmental conservation, fluid dynamics, psychology, sociology, traffic management, telecommunications, and business managers and strategists. ... Read more

Customer Reviews (1)

It's a very good intro text.
Good choice of topics. Easy to read. The concepts are well motivated. The book is full of applications. An undergraduate will be able to follow the proofs. They are clear. I also liked the homework exercises. This is a student-friendly book, as the title suggests. ... Read more

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The aim of contextual logic is to provide a formal theory of elementary logic, which is based on the doctrines of concepts, judgements, and conclusions. Concepts are mathematized using Formal Concept Analysis (FCA), while an approach to the formalization of judgements and conclusions is conceptual graphs, based on Peirce's existential graphs. Combining FCA and a mathematization of conceptual graphs yields so-called concept graphs, which offer a formal and diagrammatic theory of elementary logic.

Expressing negation in contextual logic is a difficult task. Based on the author's dissertation, this book shows how negation on the level of judgements can be implemented. To do so, cuts (syntactical devices used to express negation) are added to concept graphs. As we can express relations between objects, conjunction and negation in judgements, and existential quantification, the author demonstrates that concept graphs with cuts have the expressive power of first-order predicate logic. While doing so, the author distinguishes between syntax and semantics, and provides a sound and complete calculus for concept graphs with cuts. The author's treatment is mathematically thorough and consistent, and the book gives the necessary background on existential and conceptual graphs.

Product Description
This monograph provides an introduction to the state of the art of the probability theory that is most directly applicable to combinatorial optimization. The questions that receive the most attention are those that deal with discrete optimization problems for points in Euclidean space, such as the minimum spanning tree, the traveling-salesman tour, and minimal-length matchings. Still, there are several nongeometric optimization problems that receive full treatment, and these include the problems of the longest common subsequence and the longest increasing subsequence. The philosophy that guides the exposition is that analysis of concrete problems is the most effective way to explain even the most general methods or abstract principles. ... Read more

Customer Reviews (1)

An excellent book
My special field is neither statistics nor math. My reading this book was for research purpose. I enjoyed reading it, though it contains a few of "printing" mistakes.

The chapter 6 is somehow hard-to-find. Ibelieve Talagrand's isoperimetric theory has wide range of applications.But it is not easy to read his original article (which, besides, is morethan 100-page long). The chapter gives a very informative introduction tothe theory. ... Read more

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Includes all the basic approaches to rule based graph specification and transformation: algebraic approach, logic approach, node-based rewriting, programmed graph rewriting and 2-structures. DLC: Graph grammars. ... Read more

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Ramsey theory is the study of the structure of mathematical objects that is preserved under partitions. In its full generality, Ramsey theory is quite powerful, but can quickly become complicated. By limiting the focus of this book to Ramsey theory applied to the set of integers, the authors have produced a gentle, but meaningful, introduction to an important and enticing branch of modern mathematics. Ramsey Theory on the Integers offers students something quite rare for a book at this level: a glimpse into the world of mathematical research and the opportunity for them to begin pondering unsolved problems.

In addition to being the first truly accessible book on Ramsey theory, this innovative book also provides the first cohesive study of Ramsey theory on the integers. It contains perhaps the most substantial account of solved and unsolved problems in this blossoming subarea of Ramsey theory. The result is a breakthrough book that will engage students, teachers, and researchers alike. ... Read more

Customer Reviews (3)

An excellent book
An excellent book which requires only elementary mathematics to be understood and which is full of research problems

A Great Book
Great book about Ramsey theory.Clear it the exposition,good for the references,rare for the choice of research problems as well as for standard exercises.There are few books about Ramsey theory and this is,in my view, one of the best.

The Cutting Edge of Combinatorial Research for Undergrads!
This book did the impossible. It is a high-level research
monograph about a fascinating and very difficult part of
modern combinatorics, and yet accessible to (smart) undergraduate
students, who can start to do their own research right away.
It is beautifully written, in a crisp, lucid, and very engaging
style, and is also a masterpiece of historical scholarship with
ample notes. Thanks to this book we would get many more smart
students to go on to do a Ph.D. in math, students that otherwise would have gone elsewhere. We desperately need more such books. ... Read more

Product Description
The use of topological ideas to explore various aspects of graph theory, and vice versa, is a fruitful area of research. There are links with other areas of mathematics, such as design theory and geometry, and increasingly with such areas as computer networks where symmetry is an important feature. Other books cover portions of the material here, but there are no other books with such a wide scope. This book contains fifteen expository chapters written by acknowledged international experts in the field. Their well-written contributions have been carefully edited to enhance readability and to standardize the chapter structure, terminology and notation throughout the book. To help the reader, there is an extensive introductory chapter that covers the basic background material in graph theory and the topology of surfaces. Each chapter concludes with an extensive list of references. ... Read more