Description
This volume is a tribute to the life and mathematical work of G.A. Dirac (1925-1984). One of the leading graph theorists, he developed methods of great originality and made many fundamental discoveries.
The forty-two papers are all concerned with (or related to) Dirac's main lines of research. A number of mathematicians pay tribute to his memory by presenting new results in different areas of graph theory. Among the topics included are paths and cycles, hamiltonian graphs, vertex colouring and critical graphs, graphs and surfaces, edge-colouring, and infinite graphs.
Some of the papers were originally presented at a meeting held in Denmark in 1985. Attendance being by invitation only, some 55 mathematicians from 14 countries participated in various lectures and discussions on graph theory related to the work of Dirac. This volume contains contributions from others as well, so should not be regarded only as the proceedings of that meeting. A problems section is included, as well as a listing of Dirac's own publications.
Chapter
Chapter 3. The Edge-Distinguishing Chromatic Number of Paths and Cycles
pp.：
32 – 38
Chapter 4. On the 2-Linkage Problem for Semicomplete Digraphs
pp.：
38 – 54
Chapter 5. The Fascination of Minimal Graphs
pp.：
54 – 68
Chapter 6. Optimal Paths and Cycles in Weighted Graphs
pp.：
68 – 86
Chapter 7. A Note on Hamiltonian Graphs
pp.：
86 – 90
Chapter 8. Uniqueness of the Biggs-Smith Graph
pp.：
90 – 94
Chapter 9. Some Complete Bipartite Graph – Tree Ramsey Numbers
pp.：
94 – 106
Chapter 10. The Edge-Chromatic Class of Graphs with Maximum Degree at Least IVI – 3
pp.：
106 – 126
Chapter 11. On some Aspects of my Work with Gabriel Dirac
pp.：
126 – 132
Chapter 12. Bandwidth versus Bandsize
pp.：
132 – 146
Chapter 13. Circumference and Hamiltonism in K 1,3-Free Graphs
pp.：
146 – 156
Chapter 14. The Prism of a 2-Connected, Planar, Cubic Graph is Hamiltonian
pp.：
156 – 186
Chapter 15. A Note Concerning some Conjectures on Cyclically 4-Edge Connected 3-Regular Graphs
pp.：
186 – 194
Chapter 16. On Connectivity Properties of Eulerian Digraphs
pp.：
194 – 210
Chapter 17. Some Problems and Results on Infinite Graphs
pp.：
210 – 226
Chapter 18. On a Problem Concerning Longest Circuits in Polyhedral Graphs
pp.：
226 – 236
Chapter 19. Interpolation Theorems for the Independence and Domination Numbers of Spanning Trees
pp.：
236 – 244
Chapter 20. Ein zum Vierfarbensatz Äquivalenter Satz der Panisochromie
pp.：
244 – 270
Chapter 21.The Existence Problem for Graph Homomorphisms
pp.：
270 – 282
Chapter 22. On Edge-Colorings of Cubic Graphs and a Formula of Roger Penrose
pp.：
282 – 296
Chapter 23. Longest ab– Paths in Regular Graphs
pp.：
296 – 314
Chapter 24. On Independent Circuits in Finite Graphs and a Conjecture of Erdös and Pósa
pp.：
314 – 322
Chapter 25. Contractions to Complete Graphs
pp.：
322 – 326
Chapter 26. Triangulated Graphs with Marked Vertices
pp.：
326 – 340
Chapter 27. On a Problem upon Configurations Contained in Graphs with Given Chromatic Number
pp.：
340 – 348
Chapter 28. On Disjoint Paths in Graphs
pp.：
348 – 356
Chapter 29. Conjecture de Hadwiger: Un Graphe K-Chromatique Contraction-Critique n’est pas K-Régulier
pp.：
356 – 362
Chapter 30. A Theorem on Matchings in the Plane
pp.：
362 – 370
Chapter 31. Removing Monotone Cycles from Orientations
pp.：
370 – 378
Chapter 32. Disentangling Pairings in Trees
pp.：
378 – 386
Chapter 33. Colour-Critical Graphs with Vertices of Low Valency
pp.：
386 – 412
Chapter 34. About the Chromatic Number of 1-Embeddable Graphs
pp.：
412 – 416
Chapter 35. Problems and Conjectures in the Combinatorial Theory of Ordered Sets
pp.：
416 – 432
Chapter 36. A Proof of Kuratowski’s Theorem
pp.：
432 – 436
Chapter 37. Finite and Infinite Graphs whose Spanning Trees are Pairwise Isomorphic
pp.：
436 – 452
Chapter 38. Bridges of Longest Circuits Applied to the Circumference of Regular Graphs
pp.：
452 – 468
Chapter 39. On a Standard Method Concerning Embeddings of Graphs
pp.：
468 – 488
Chapter 40. Construction of Critical Graphs by Replacing Edges
pp.：
488 – 502
Chapter 41. A Brief History of Hamiltonian Graphs
pp.：
502 – 512
Chapter 42. Erinnerungen an Gabriel Dirac in Hamburg
pp.：
512 – 514
Chapter 43. Hamilton Paths in Multipartite Oriented Graphs
pp.：
514 – 530
Chapter 44. Problems
pp.：
530 – 534
Graph Theory in Memory of G.A. Dirac
( Volume 41 )
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