The techniques of graph theory have been used in solving many classical problems. This book explores the field's classical foundations and its developing theories, ideas and applications to new problems. It also examines the geometric properties of graph theory and its widening uses in combinatorial optimization theory and application.
Dealing with graph theory, this book includes chapters on measurement and analytic graph theory. It takes a comprehensive approach to graph theory that integrates an exposition of classical developments with various methods, models, and practical needs.
Graph theory is a flourishing discipline containing a body of beautiful and powerful theorems of wide applicability. This book provides a systematic treatment of the theory of graphs. It describes and illustrates commonly used proof techniques, and presents exercises - of varying levels of difficulty - to help the reader master the techniques.
The fourth edition of this standard textbook of modern graph theory has been revised, updated, and substantially extended. Covering all major recent developments, it can be used both as a reliable textbook for an introductory course and as a graduate text.
Offers an introduction to the analysis and design of dynamic multiagent networks. Focusing on graph theoretic methods for the analysis and synthesis of dynamic multiagent networks, this book presents a fresh formalism and set of tools for networked systems.
Drawing on many years' experience of teaching discrete mathematics to students, the author introduces such aspects as enumeration, graph theory and configurations or arrangements. Starting with an introduction to counting and related problems, he moves on to the basic ideas of graph theory with particular emphasis on trees and planar graphs.
Deals with two important branches of graph theory - factor theory and extendable graphs. This book includes basic techniques, theoretical foundations, as well as the advances in the field. It discusses open problems and conjectures to inspire the readers. It is suitable for researchers and graduate students in graph theory and combinatorics.
Includes a solution to the 4m-conjecture of Erdos/Ko/Rado 1938, an answer to a question of Erdos (1962) in combinatorial number theory, and the discovery that the AD-inequality implies more general and sharper number theoretical inequalities than for instance Behrend's inequality.
Buildings are combinatorial constructions successfully exploited to study groups of various types. The vertex set of a building can be naturally decomposed into subsets called Grassmannians. The book contains results on Grassmannians of buildings of classical types.
Covers the fundamentals of pure mathematical combinatorics, including combinations, permutations, and more sophisticated counting techniques; generating functions; difference equations; generalizations; and, special functions. This title also presents graph-theoretic terminology and elementary graph theory as it arises in combinatorics.
This major revision of James Oxley's classic Matroid Theory provides a comprehensive introduction to the subject, covering the basics to more advanced topics. With over 700 exercises and proofs of all relevant major theorems, this book is the ideal reference and class text for academics and graduate students in mathematics and computer science.
Based on the contributions to Laszlo Lovasz's 60th anniversary, Fete of Combinatorics and Computer Science provides a collection of articles on discrete mathematics and theoretical computer science. Readers will find a discussion of the state-of-the-art in the field.
Ramsey theory is an area of combinatorics with deep connections to other fields of mathematics such as topological dynamics, ergodic theory, mathematical logic, and algebra. This book presents a method for building higher-dimensional Ramsey spaces from basic one-dimensional principles.
Focuses on graph theory, with an emphasis on topics relating to linear algebra and matrix theory. This title includes topics those of graph theory such as regular graphs and algebraic connectivity, Laplacian eigenvalues of threshold graphs, positive definite completion problem and graph-based matrix games.
Written for advanced undergraduate and beginning graduate students, this book provides a wide range of examples along with historical discussions of mathematicians, problems, and conjectures. It covers topics such as toughness, graph minors, perfect graphs, list colorings, nowhere zero flows, list edge colorings, and the rainbow number of a graph.
Written by the author of the lattice system, this book describes lattice in considerable depth. It begins with the essentials and systematically delves into specific low levels details as necessary. Numerous examples using data sets from various R packages are included.
Combining analytic analysis of network reliability with the study of network combinatorial properties, this book develops analytic, combinatorial, and Monte Carlo models, methods, and algorithms. It examines optimal network synthesis, network exit time, and networks whose elements have random lifetimes.
This book covers the theory of subdivision curves in detail, which is a prerequisite for that of subdivision surfaces. It then considers how those analyses can be used in reverse to design a scheme best matching the particular criteria for a given application.
Suitable for an introductory combinatorics course lasting one or two semesters, this book includes an extensive list of problems, ranging from routine exercises to research questions. It walks the reader through the classic parts of combinatorial enumeration and graph theory, while also discussing some the progress made in the area.
The book integrates approaches from mathematics, physics and computer sciences to analyse the organisation of complex networks. Every organisational principle of networks is defined, quantified and then analysed for its influences on the properties and functions of molecular, biological, ecological and social networks.
Covers applications of graph theory in the area of power systems. This book introduces the basic concepts of graph theory, major properties, theorems, and algorithms in graph theory and network flow programming. It deals with the practical application of graph theory and network flow programming to all kinds of power systems problems.
The Second Waterloo Workshop on Computer Algebra was dedicated to the 70th birthday of combinatorics pioneer Georgy Egorychev. This book of formally-refereed papers submitted after that workshop covers topics closely related to Egorychev's influential works.
Sets out a body of mathematical theory for finite graphs with nodes placed randomly in Euclidean space and edges added to connect points that are close to each other. Suitable for graduate students and researchers in probability, and combinatorics, this book covers topics such as edge and component counts, vertex degrees, cliques, and more.
One of the features of contemporary additive combinatorics is the interplay of a great variety of mathematical techniques, including combinatorics, harmonic analysis, convex geometry, graph theory, probability theory, algebraic geometry or ergodic theory. This book gathers the contributions of some of the leading researchers in the combinatorics.
* The material has been extensively class-tested for over ten years at both the author's own university and other institutions. * The book is uniquely organized into two main sections, one on Fibonacci Numbers and one on Catalan Numbers, each containing subsections that explore related topics in intricate detail.
This book introduces the theory of graphs and random walks on graphs, covers methods for exploring the structure of finite connected graphs and databases, and details applications in electric resistance networks, urban planning, linguistic databases and more.
Including hundreds of worked examples and exercises with solutions, this volume focuses on the application of central mathematical topics such as linear algebra, group theory and complex analysis. Well designed diagrams and illustrations aid comprehension.
This comprehensive textbook on combinatorial optimization emphasizes theoretical results and algorithms with provably good performance, in contrast to heuristics. The text contains complete but concise proofs, and also provides numerous exercises and references.
Suitable for self-study or a first course in combinatorics at the undergraduate level, this title focuses on counting problems and emphasizes a problem solving approach. It includes a chapter on graph theory and exercises, some with full solutions or hints.
Deals with the basic subjects of design theory. This book begins with balanced incomplete block designs, and describes various constructions of these designs. It includes finite projective and affine planes, difference sets and Hadamard matrices, as tools to construct balanced incomplete block designs. It treats orthogonal latin squares.
Graph Theory is an important area of contemporary mathematics with many applications in computer science, genetics, chemistry, engineering, industry, business and in social sciences. This book discusses the key concepts of graph theory with emphasis on trees, bipartite graphs, cycles, chordal graphs, planar graphs and graph colouring.
Constitutes the refereed proceedings of the 5th International Workshop on Visualization for Cyber Security held on September 15, 2008, in Cambridge, Massachusetts, USA, in conjunction with the 11th International Symposium on Recent Advances in Intrusion Detection (RAID). This book presents 18 reviewed and selected papers from 27 submissions.
Endre Szemeredi's influence on today's mathematics, especially in combinatorics, additive number theory, and theoretical computer science, is enormous. This volume is a celebration of his achievements and personality, on the occasion of his 70th birthday.
Focuses on combinatorial problems in mathematical competitions. This work provides basic knowledge on how to solve combinatorial problems in mathematical competitions, and also introduces solutions to combinatorial problems and some typical problems with often-used solutions.
Discrete probability theory and the theory of algorithms have become close partners over the years. This volume contains papers that address the developments in this field. They are from the IMA Workshops "Probability and Algorithms" and "The Finite Markov Chain Renaissance." It is useful for researchers and graduate students.
The creation of the science on stem cells and development of its theoretical bases is a prevalent topic, considering evolutionary cell biology and the cardinal problem of the developmental biology. This book examines the system of non-traditional ideas about the nature and role of stem cells in ontogenesis, reproduction and evolution of plants.
Provides an overview of polyhedral methods and efficient algorithms in combinatorial optimization. This work features methods that form a coherent and powerful kernel in combinatorial optimization, with strong links to discrete mathematics, mathematical programming and computer science.
With an emphasis on mathematical thinking and problem solving, this work shows how discrete probability, statistics, and elementary discrete mathematics are used in games, sports, and gambling situations. It draws on numerous examples, questions, and problems to explain the application of mathematical theory to various real-life games.