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Last Edited
13 Sep 2009

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© 1999-2009
Aaron D. Gross
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Graph Theory Textbooks and Resources

FEATURES

• Provides a unified, up-to-date resource on graph theory
• Explores the algorithmic and optimization approaches of graph theory as well as "pure" graph theory
• Unifies the diversity of graph theory terminology and notation
• Bridges theory and practice with many easy-to-read algorithms

Includes a glossary in each chapter-more than 1000 entries in total

PUBLISHER'S DESCRIPTION
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.

See also the Index from the Handbook of Graph Theory.

TABLE OF CONTENTS

1. INTRODUCTION TO GRAPHS

1.1 Fundamentals of Graph Theory, Jonathan L. Gross and Jay Yellen
1.2 Families of Graphs and Digraphs, Lowell W. Beineke
1.3 History of Graph Theory, Robin J. Wilson
Glossary

2. GRAPH REPRESENTATION

2.1 Computer Representation of Graphs, Alfred V. Aho
2.2 The Graph Isomorphism Problem, Mark Goldberg
2.3 The Reconstruction Problem, Josef Lauri
2.4 Recursively Constructed Graphs, R.B. Borie, R. Gary Parker, and C.A. Tovey
Glossary

3. DIRECTED GRAPHS

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

4. CONNECTIVITY AND TRAVERSABILITY

4.1 Connectivity: Properties and Structure, Josep Fàbrega and Miguel Angel Fiol
4.2 Eulerian Graphs, Herbert Fleischner
4.3 Chinese Postman Problems, R. Gary Parker
4.4 DeBruijn Graphs and Sequences, A.K. Dewdney
4.5 Hamiltonian Graphs, Ronald J. Gould
4.6 Traveling Salesman Problems, Gregory Gutin
4.7 Further Topics in Connectivity, Josep Fàbrega and Miguel Angel Fiol
Glossary

5. COLORINGS AND RELATED TOPICS

5.1 Graph Coloring, Zsolt Tuza
5.2 Further Topics in Graph Coloring, Zsolt Tuza
5.3 Independent Sets and Cliques, Gregory Gutin
5.4 Factors and Factorization, Michael Plummer
5.5 Perfect Graphs, Alan Tucker
5.6 Applications to Timetabling, Edmund Burke, Dominique de Werra, and Jeffrey Kingston
Glossary

6. ALGEBRAIC GRAPH THEORY

6.1 Automorphisms, Mark E. Watkins
6.2 Cayley Graphs, Brian Alspach
6.3 Enumeration, Paul K. Stockmeyer
6.4 Graphs and Vector Spaces, Krishnaiyan "KT" Thulasiraman
6.5 Spectral Graph Theory, Michael Doob
6.6 Matroidal Methods in Graph Theory, James Oxley
Glossary

7. TOPOLOGICAL GRAPH THEORY

7.1 Graphs on Surfaces, Tomaz Pisanski and Primoz Potocnik
7.2 Minimum and Maximum Imbeddings, Jianer Chen
7.3 Genus Distribution, Jonathan L. Gross
7.4 Voltage Graphs, Jonathan L. Gross
7.5 Genus of a Group, Thomas W. Tucker
7.6 Maps, Andrew Vince
7.7 Representativity, Dan Archdeacon
7.8 Triangulations, Seiya Negami
7.9 Graphs and Finite Geometries, Arthur T. White
Glossary

8.0 ANALYTIC GRAPH THEORY

8.1 Extremal Graph Theory, Bela Bollobas and Vladimir Nikiforov
8.2 Random Graphs, Nicholas Wormald
8.3 Ramsey Graph Theory, Ralph Faudree
8.4 Probabilistic Methods, Alan Frieze
Glossary

9.0 GRAPHICAL MEASUREMENT

9.1 Distance in Graphs, Gary Chartrand and Ping Zhang
9.2 Domination in Graphs, Teresa W. Haynes and Michael A. Henning
9.3 Tolerance Graphs, F.R. McMorris
9.4 Bandwidth, Robert C. Brigham
Glossary

10. GRAPHS IN COMPUTER SCIENCE

10.1 Searching, Harold N. Gabow
10.2 Dynamic Graph Algorithms, C. Demetrescu, I. Finocchi, and G.F. Italiano
10.3 Drawings of Graphs, Giuseppe Liotta and Roberto Tamassia
10.4 Algorithms on Recursively Constructed Graphs, R.B. Borie, R. Gary Parker, and C.A. Tovey
Glossary

11. NETWORKS AND FLOWS

11.1 Maximum Flows, Clifford Stein
11.2 Minimum Cost Flows, Lisa Fleischer
11.3 Matchings and Assignments, Douglas R. Shier
11.4 Communication Networks, Prakash Mirchandani and David Simchi-Levi
Glossary