Graph Theory in Memory of G.A. Dirac

L. Døvling Andersen, I. Tafteberg Jakobsen, P. Vestergaard, B. Toft, C. Thomassen

• Publisher: North Holland
• Year: 1988
• Print ISBN:
  9780444871299
• eBook ISBN:
  9780080867816
• Topic: Matematica
• Subtopic: Matematica discreta

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.

Table of contents

• Front Cover
• Graph Theory in Memory of G.A. Dirac
• Copyright Page
• Contents
• Preface
• Chapter 1. Gabriel Andrew Dirac
• Chapter 2. Hamilton Cycles in Metacirculant Graphs with Prime Power Cardinal Blocks
• Chapter 3. The Edge-Distinguishing Chromatic Number of Paths and Cycles
• Chapter 4. On the 2-Linkage Problem for Semicomplete Digraphs
• Chapter 5. The Fascination of Minimal Graphs
• Chapter 6. Optimal Paths and Cycles in Weighted Graphs
• Chapter 7. A Note on Hamiltonian Graphs
• Chapter 8. Uniqueness of the Biggs-Smith Graph
• Chapter 9. Some Complete Bipartite Graph – Tree Ramsey Numbers
• Chapter 10. The Edge-Chromatic Class of Graphs with Maximum Degree at Least IVI – 3
• Chapter 11. On some Aspects of my Work with Gabriel Dirac
• Chapter 12. Bandwidth versus Bandsize
• Chapter 13. Circumference and Hamiltonism in K 1,3-Free Graphs
• Chapter 14. The Prism of a 2-Connected, Planar, Cubic Graph is Hamiltonian
• Chapter 15. A Note Concerning some Conjectures on Cyclically 4-Edge Connected 3-Regular Graphs
• Chapter 16. On Connectivity Properties of Eulerian Digraphs
• Chapter 17. Some Problems and Results on Infinite Graphs
• Chapter 18. On a Problem Concerning Longest Circuits in Polyhedral Graphs
• Chapter 19. Interpolation Theorems for the Independence and Domination Numbers of Spanning Trees
• Chapter 20. Ein zum Vierfarbensatz Äquivalenter Satz der Panisochromie
• Chapter 21.The Existence Problem for Graph Homomorphisms
• Chapter 22. On Edge-Colorings of Cubic Graphs and a Formula of Roger Penrose
• Chapter 23. Longest ab– Paths in Regular Graphs
• Chapter 24. On Independent Circuits in Finite Graphs and a Conjecture of Erdös and Pósa
• Chapter 25. Contractions to Complete Graphs
• Chapter 26. Triangulated Graphs with Marked Vertices
• Chapter 27. On a Problem upon Configurations Contained in Graphs with Given Chromatic Number
• Chapter 28. On Disjoint Paths in Graphs
• Chapter 29. Conjecture de Hadwiger: Un Graphe K-Chromatique Contraction-Critique n’est pas K-Régulier
• Chapter 30. A Theorem on Matchings in the Plane
• Chapter 31. Removing Monotone Cycles from Orientations
• Chapter 32. Disentangling Pairings in Trees
• Chapter 33. Colour-Critical Graphs with Vertices of Low Valency
• Chapter 34. About the Chromatic Number of 1-Embeddable Graphs
• Chapter 35. Problems and Conjectures in the Combinatorial Theory of Ordered Sets
• Chapter 36. A Proof of Kuratowski’s Theorem
• Chapter 37. Finite and Infinite Graphs whose Spanning Trees are Pairwise Isomorphic
• Chapter 38. Bridges of Longest Circuits Applied to the Circumference of Regular Graphs
• Chapter 39. On a Standard Method Concerning Embeddings of Graphs
• Chapter 40. Construction of Critical Graphs by Replacing Edges
• Chapter 41. A Brief History of Hamiltonian Graphs
• Chapter 42. Erinnerungen an Gabriel Dirac in Hamburg
• Chapter 43. Hamilton Paths in Multipartite Oriented Graphs
• Chapter 44. Problems