Graph theory, as a recognized discipline, is a relative newcomer to mathematics. The first formal paper is found in the work of Leonard Euler in 1736. In recent years the subject has grown so rapidly that in today's literature, graph theory papers abound with mathematical developments and significant applications. As with any academic field, it is good to step back occasionally and ask "Where is all this activity taking us?", "What are the outstanding fundamental problems?", "What are the next important steps to take?" In short, "Quo vadis, graph theory?". The contributors to this volume aim, together, to provide a comprehensive reference source for future directions and open questions in the field.
Author(s): John Gimbel, John W. Kennedy and Louis V. Quintas (Eds.)
Series: Annals of Discrete Mathematics 55
Publisher: North-Holland
Year: 1993
Language: English
Pages: ii-vi, 1-397
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
