Quo Vadis, Graph Theory? (eBook)

A Source Book for Challenges and Directions

J. Gimbel, J.W. Kennedy, L.V. Quintas (Herausgeber)

eBook Download: PDF

1993 | 1. Auflage
396 Seiten
Elsevier Science (Verlag)
978-0-08-086795-3 (ISBN)

Infos

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.

Inhalt

Front Cover 1
Quo Vadis, Graph Theory? 4
Copyright Page 5
CONTENTS 8
Foreword 6
Chapter 1. Whither graph theory? 10
Chapter 2. The future of graph theory 14
Chapter 3. New directions in graph theory (with an emphasis on the role of applications) 22
Chapter 4. A survey of (m,k)-colorings 54
Chapter 5. Numerical decks of trees 68
Chapter 6. The complexity of colouring by infinite vertex transitive graphs 80
Chapter 7. Rainbow subgraphs in edge-colorings of complete graphs 90
Chapter 8. Graphs with special distance properties 98
Chapter 9. Probability models for random multigraphs with applications in cluster analysis 102
Chapter 10. Solved and unsolved problems in chemical graph theory 118
Chapter 11. Detour distance in graphs 136
Chapter 12. Integer-distance graphs 146
Chapter 13. Toughness and the cycle structure of graphs 154
Chapter 14. The Birkhoff-Lewis equations for graph-colorings 162
Chapter 15. The complexity of knots 168
Chapter 16. The impact of F-polynomials in graph theory 182
Chapter 17. A note on well-covered graphs 188
Chapter 18. Cycle covers and cycle decompositions of graphs 192
Chapter 19. Matching extensions and products of graphs 200
Chapter 20. Prospects for graph theory algorithms 210
Chapter 21. The state of the three color problem 220
Chapter 22. Ranking planar embeddings using PQ-trees 258
Chapter 23. Some problems and results in cochromatic theory 270
Chapter 24. From random graphs to graph theory 274
Chapter 25. Matching and vertex packmg: How “hard”are they? 284
Chapter 26. The competition number and its variants 322
Chapter 27. Which double starlike trees span ladders? 336
Chapter 28. The random ƒ-graph process 342
Chapter 29. Quo vadis, random graph theory? 350
Chapter 30. Exploratory statistical analysis of networks 358
Chapter 31. The Hamiltonian decomposition of certain circulant graphs 376
Chapter 32. Discovery-method teaching in graph theory 384
Chapter 33. Index of Key Terms 394

Produkt-Details

• Erscheint lt. Verlag: 17.3.1993
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Finanz- / Wirtschaftsmathematik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Graphentheorie
• Themenwelt: Technik
• ISBN-10: 0-08-086795-2 / 0080867952
• ISBN-13: 978-0-08-086795-3 / 9780080867953