Handbook of Graph Theory
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Summary
The Handbook of Graph Theory is the most comprehensive single-source guide to graph theory ever published. Best-selling authors Jonathan Gross and Jay Yellen assembled an outstanding team of experts to contribute overviews of more than 50 of the most significant topics in graph theory-including those related to algorithmic and optimization approaches as well as "pure" graph theory. They then carefully edited the compilation to produce a unified, authoritative work ideal for ready reference.
Designed and edited with non-experts in mind, the Handbook of Graph Theory makes information easy to find and easy to understand. The treatment of each topic includes lists of essential definitions and facts accompanied by examples, tables, remarks, and in some areas, conjectures and open problems. Each section contains a glossary of terms relevant to that topic and an extensive bibliography of references that collectively form an extensive guide to the primary research literature.
The applications of graph theory are fast becoming ubiquitous. Whether your primary area of interest lies in mathematics, computer science, engineering, or operations research, this handbook holds the key to unlocking graph theory's intricacies, applications, and potential.
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
The Graph Isomorphism Problem, Mark Goldberg
The Reconstruction Problem, Josef Lauri
Recursively Constructed Graphs, R.B. Borie, R. Gary Parker, and C.A. Tovey
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, Josep Fàbrega and Miguel Angel Fiol
Eulerian Graphs, Herbert Fleischner
Chinese Postman Problems, R. Gary Parker
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
Independent Sets and Cliques, Gregory Gutin
Factors and Factorization, Michael Plummer
Perfect Graphs, Alan Tucker
Applications to Timetabling, Edmund Burke, Dominique de Werra, and Jeffrey Kingston
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 and Maximum Imbeddings, Jianer Chen
Genus Distribution, Jonathan L. Gross
Voltage Graphs, Jonathan L. Gross
Genus of a Group, Thomas W. Tucker
Maps, Andrew Vince
Representativity, Dan Archdeacon
Triangulations, Seiya Negami
Graphs and Finite Geometries, Arthur T. White
ANALYTIC GRAPH THEORY
Extremal Graph Theory, Bela Bollobas and Vladimir Nikiforov
Random Graphs, Nicholas Wormald
Ramsey Graph Theory, Ralph Faudree
Probabilistic Methods, Alan Frieze
GRAPHICAL MEASUREMENT
Distance in Graphs, Gary Chartrand and Ping Zhang
Domination in Graphs, Teresa W. Haynes and Michael A. Henning
Tolerance Graphs, F.R. McMorris
Bandwidth, Robert C. Brigham
GRAPHS IN COMPUTER SCIENCE
Searching, Harold N. Gabow
Dynamic Graph Algorithms, C. Demetrescu, I. Finocchi, and G.F. Italiano
Drawings of Graphs, Giuseppe Liotta and Roberto Tamassia
Algorithms on Recursively Constructed Graphs, R.B. Borie, R. Gary Parker, and C.A. Tovey
NETWORKS AND FLOWS
Maximum Flows, Clifford Stein
Minimum Cost Flows, Lisa Fleischer
Matchings and Assignments, Douglas R. Shier
Communication Network Design Models, Prakash Mirchandani and David Simchi-Levi
Editorial Reviews
"[This] is 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. …. Summing Up: Highly recommended."
- CHOICE, January 2005, Vol. 42, No. 05
