Quo Vadis, Graph Theory? : A Source Book for

Graph Theory (as a recognized discipline) is a relative newcomer to Mathematics. The first formal paper is found in the work of Leonhard Euler in 1736. In recent years the subject has grown so rapidly that in today's literature, graph theory papers abound with new 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 have together provided a comprehensive reference source for future directions and open questions in the field.

Foreword
Whither graph theory?	p. 1
The future of graph theory	p. 5
New directions in graph theory (with an emphasis on the role of applications)	p. 13
A survey of (m,k)-colorings	p. 45
Numerical decks of trees	p. 59
The complexity of colouring by infinite vertex transitive graphs	p. 71
Rainbow subgraphs in edge-colorings of complete graphs	p. 81
Graphs with special distance properties	p. 89
Probability models for random multigraphs with applications in cluster analysis	p. 93
Solved and unsolved problems in chemical graph theory	p. 109
Detour distance in graphs	p. 127
Integer-distance graphs	p. 137
Toughness and the cycle structure of graphs	p. 145
The Birkhoff-Lewis equations for graph-colorings	p. 153
The complexity of knots	p. 159
The impact of F-polynomials in graph theory	p. 173
A note on well-covered graphs	p. 179
Cycle covers and cycle decompositions of graphs	p. 183
Matching extensions and products of graphs	p. 191
Prospects for graph theory algorithms	p. 201
The state of the three color problem	p. 211
Ranking planar embeddings using PQ-trees	p. 249
Some problems and results in cochromatic theory	p. 261
From random graphs to graph theory	p. 265
Matching and vertex packing: How "hard" are they?	p. 275
The competition number and its variants	p. 313
Which double starlike trees span ladders?	p. 327
The random f-graph process	p. 333
Quo vadis, random graph theory?	p. 341
Exploratory statistical analysis of networks	p. 349
The Hamiltonian decomposition of certain circulant graphs	p. 367
Discovery-method teaching in graph theory	p. 375
Index of Key Terms	p. 385
Table of Contents provided by Blackwell. All Rights Reserved.

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

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