Quo Vadis, Graph Theory?A Source Book for Challenges and Directions

Content: 
Advisory Editors
Page ii

Edited by
Page iii

Copyright page
Page iv

Foreword
Pages v-vi
John Gimbel, John W. Kennedy, Louis V. Quintas

Whither Graph Theory? Original Research Article
Pages 1-3
William T. Tutte

The Future of Graph Theory Original Research Article
Pages 5-11
Bela Bollobás

New Directions in Graph Theory (With an Emphasis on the Role of Applications) Original Research Article
Pages 13-43
Fred S. Roberts

A Survey of (m, k)-Colorings Original Research Article
Pages 45-57
Marietjie Frick

Numerical Decks of Trees Original Research Article
Pages 59-69
Fanica Gavril, Ilia Krasikov, Johanan Schönheim

The Complexity of Colouring by Infinite Vertex Transitive Graphs Original Research Article
Pages 71-79
Bruce Bauslaugh

Rainbow Subgraphs in Edge-Colorings of Complete Graphs Original Research Article
Pages 81-88
Paul Erdős, Zsolt Tuza

Graphs with Special Distance Properties Original Research Article
Pages 89-92
Martin Lewinter

Probability Models for Random Multigraphs with Applications in Cluster Analysis Original Research Article
Pages 93-108
Erhard A.J. Godehardt

Solved and Unsolved Problems in Chemical Graph Theory Original Research Article
Pages 109-126
Alexandru T. Balaban

Detour Distance in Graphs Original Research Article
Pages 127-136
Gary Chartrand, Garry L. Johns, Songlin Tian

Integer-Distance Graphs Original Research Article
Pages 137-144
Ralph P. Grimaldi

Toughness and the Cycle Structure of Graphs Original Research Article
Pages 145-151
Douglas Bauer, Edward Schmeichel

The Birkhoff-Lewis Equations for Graph-Colorings Original Research Article
Pages 153-158
William T. Tutte

The Complexity of Knots Original Research Article
Pages 159-171
Dominic J.A. Welsh

The Impact of F-polynomials in Graph Theory Original Research Article
Pages 173-178
Edward J. Farrell

A Note on Well-Covered Graphs Original Research Article
Pages 179-181
Václav Chvátal, Peter J. Slater

Cycle Covers and Cycle Decompositions of Graphs Original Research Article
Pages 183-189
Cun-Quan Zhang

Matching Extensions and Products of Graphs Original Research Article
Pages 191-200
Jiping Liu, Qinglin Yu

Prospects for Graph Theory Algorithms Original Research Article
Pages 201-210
Ronald C. Read

The State of the Three Color Problem Original Research Article
Pages 211-248
Richard Steinberg

Ranking Planar Embeddings Using PQ-Trees Original Research Article
Pages 249-260
Almira Karabeg

Some Problems and Results in Cochromatic Theory Original Research Article
Pages 261-264
Paul Erdós, John Gimbel

From Random Graphs to Graph Theory Original Research Article
Pages 265-273
Andrzej Ruciński

Matching and Vertex Packing: How “hard” are They? Original Research Article
Pages 275-312
Michael D. Plummer

The Competition Number and its Variants Original Research Article
Pages 313-326
Suh-Ryung Kim

Which Double Starlike Trees Span Ladders? Original Research Article
Pages 327-331
Martin Lewinter, William F. Widulski

The Random f-Graph Process Original Research Article
Pages 333-339
Krystyna T. BalińSka, Louis V. Quintas

Quo Vadis, Random Graph Theory? Original Research Article
Pages 341-348
Edgar M. Palmer

Exploratory Statistical Anlaysis of Networks Original Research Article
Pages 349-365
Ove Frank, Krzysztof Nowicki

The Hamiltonian Decomposition of Circulant Graphs Original Research Article
Pages 367-373
Jiping Liu

Discovery-Method Teaching in Graph Theory Original Research Article
Pages 375-384
Phyllis Zweig Chinn

Index of Key Terms
Pages 385-397