Handbook of Graph Theory, Second Edition

Handbook of Graph Theory, Second Edition

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Features

  • Covers new topics in pure and applied graph theory
  • Includes 65 self-contained chapters organized into 13 parts
  • Bridges theory and practice with many easy-to-read algorithms
  • Unifies the diversity of graph theory terminology and notation
  • Provides a glossary and references at the end of each chapter

Summary

In the ten years since the publication of the best-selling first edition, more than 1,000 graph theory papers have been published each year. Reflecting these advances, Handbook of Graph Theory, Second Edition provides comprehensive coverage of the main topics in pure and applied graph theory. This second edition—over 400 pages longer than its predecessor—incorporates 14 new sections.

Each chapter includes lists of essential definitions and facts, accompanied by examples, tables, remarks, and, in some cases, conjectures and open problems. A bibliography at the end of each chapter provides an extensive guide to the research literature and pointers to monographs. In addition, a glossary is included in each chapter as well as at the end of each section. This edition also contains notes regarding terminology and notation.

With 34 new contributors, this handbook is the most comprehensive single-source guide to graph theory. It emphasizes quick accessibility to topics for non-experts and enables easy cross-referencing among chapters.

Table of Contents

Introduction to Graphs
Fundamentals of Graph Theory, Jonathan L. Gross and Jay Yellen
Families of Graphs and Digraphs, Lowell W. Beineke
History of Graph Theory, Robin J. Wilson

Graph Representation
Computer Representation of Graphs, Alfred V. Aho
Graph Isomorphism, Brendan D. McKay
The Reconstruction Problem, Josef Lauri
Recursively Constructed Graphs, Richard B. Borie, R. Gary Parker, and Craig A. Tovey
Structural Graph Theory, Maria Chudnovsky

Directed Graphs
Basic Digraph Models and Properties, Jay Yellen
Directed Acyclic Graphs, Stephen B. Maurer
Tournaments, K.B. Reid

Connectivity and Traversability
Connectivity Properties and Structure, Camino Balbuena, Josep Fàbrega, and Miguel Angel Fiol
Eulerian Graphs, Herbert Fleischner
Chinese Postman Problems, R. Gary Parker and Richard B. Borie
DeBruijn Graphs and Sequences, A.K. Dewdney
Hamiltonian Graphs, Ronald J. Gould
Traveling Salesman Problems, Gregory Gutin
Further Topics in Connectivity, Josep Fàbrega and Miguel Angel Fiol

Colorings and Related Topics
Graph Coloring, Zsolt Tuza
Further Topics in Graph Coloring, Zsolt Tuza
Independence and Cliques, Gregory Gutin
Factors and Factorization, Michael Plummer
Applications to Timetabling, Edmund Burke, Dominique de Werra, and Jeffrey Kingston
Graceful Labelings, Joseph A. Gallian

Algebraic Graph Theory
Automorphisms, Mark E. Watkins
Cayley Graphs, Brian Alspach
Enumeration, Paul K. Stockmeyer
Graphs and Vector Spaces, Krishnaiyan "KT" Thulasiraman
Spectral Graph Theory, Michael Doob
Matroidal Methods in Graph Theory, James Oxley

Topological Graph Theory
Graphs on Surfaces, Tomaz Pisanski and Primoz Potocnik
Minimum Genus and Maximum Genus, Jianer Chen
Genus Distributions, Jonathan L. Gross
Voltage Graphs, Jonathan L. Gross
The Genus of a Group, Thomas W. Tucker
Maps, Roman Nedela and Martin Skoviera
Representativity, Dan Archdeacon
Triangulations, Seiya Negami
Graphs and Finite Geometries, Arthur T. White
Crossing Numbers, R. Bruce Richter and Gelasio Salazar

Analytic Graph Theory
Extremal Graph Theory, Bela Bollobas and Vladimir Nikiforov
Random Graphs, Nicholas Wormald
Ramsey Graph Theory, Ralph J. Faudree
The Probabilistic Method, Alan Frieze and Po-Shen Loh
Graph Limits, Bojan Mohar

Graphical Measurement
Distance in Graphs, Gary Chartrand and Ping Zhang
Domination in Graphs, Teresa W. Haynes and Michael A. Henning
Tolerance Graphs, Martin Charles Golumbic
Bandwidth, Robert C. Brigham
Pursuit-Evasion Problems, Richard B. Borie, Sven Koenig, and Craig A. Tovey

Graphs in Computer Science
Searching, Harold N. Gabow
Dynamic Graph Algorithms, Camil Demetrescu, Irene Finocchi, and Giuseppe F. Italiano
Drawings of Graphs, Emilio Di Giacomo, Giuseppe Liotta, and Roberto Tamassia
Algorithms on Recursively Constructed Graphs, Richard B. Borie, R. Gary Parker, and Craig A. Tovey
Fuzzy Graphs, John N. Mordeson and D.S. Malik
Expander Graphs, Mike Krebs and Anthony Shaheen
Visibility Graphs, Alice M. Dean and Joan P. Hutchinson

Networks and Flows
Maximum Flows, Clifford Stein
Minimum Cost Flows, Lisa Fleischer
Matchings and Assignments, Jay Sethuraman and Douglas R. Shier

Communication Networks
Complex Networks, Anthony Bonato and Fan Chung
Broadcasting and Gossiping, Hovhannes A. Harutyunyan, Arthur L. Liestman, Joseph G. Peters, and Dana Richards
Communication Network Design Models, Prakash Mirchandani and David Simchi-Levi
Network Science for Graph Theorists, David C. Arney and Steven B. Horton

Natural Science and Processes
Chemical Graph Theory, Ernesto Estrada and Danail Bonchev
Ties between Graph Theory and Biology, Jacek Blazewicz, Marta Kasprzak, and Nikos Vlassis

Index

A Glossary appears at the end of each chapter.

Editor Bio(s)

Jonathan Gross is a professor of computer science at Columbia University. A recipient of numerous awards and research grants, Dr. Gross is the coauthor of several books and the inventor of the voltage graph, a construct widely used in topological graph theory and other areas. His current research interests include the genus distribution of graphs, computer graphics, and knot theory.

Jay Yellen is the Archibald Granville Bush Professor of Mathematics at Rollins College, where he has received several teaching and research awards. Dr. Yellen has coauthored one book with Dr. Gross, written materials for IBM courses, and conducted workshops for secondary-school mathematics teachers. His current research interests include graph theory, discrete optimization, and graph algorithms for software testing and course timetabling.

Ping Zhang is a professor of mathematics at Western Michigan University. Dr. Zhang has coauthored five books. Her research interests include algebraic combinatorics and colorings, distance and convexity, traversability, decompositions, and domination within graph theory.

Editorial Reviews

Praise for the First Edition:
… a fine guide to various literatures, especially for topics like Ramsey theory … . Many first-rate mathematicians have contributed, making the exposition's quality high overall. …. Highly recommended.
CHOICE, January 2005, Vol. 42, No. 05

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