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.
Author(s): Lars Dovling Andersen, Ivan Tafteberg Jakobsen, Carsten Thomassen, Bjarne Toft and Preben Dahl Vestergaard (Eds.)
Series: Annals of discrete mathematics 41
Publisher: North-Holland; Sole distributors for the U.S.A. and Canada, Elsevier Science Pub. Co
Year: 1989
Language: English
Pages: ii-vi, 1-517
City: Amsterdam; New York :, New York, N.Y., U.S.A
Content:
General Editor
Page ii
Edited by
Page iii
Copyright page
Page iv
Preface
Pages v-vi
Lars Døvling Andersen, Ivan Tafteberg Jakobsen, Carsten Thomassen, Bjarne Toft, Preben Dahl Vestergaard
Gabriel Andrew Dirac
Pages 1-6
Hamilton Cycles in Metacirculant Graphs with Prime Power Cardinal Blocks Original Research Article
Pages 7-16
B. Alspach
The Edge-Distinguishing Chromatic Number of Paths and Cycles Original Research Article
Pages 17-22
K. Al-Wahabi, R. Bari, F. Harary, D. Ullman
On the 2-Linkage Problem for Semicomplete Digraphs Original Research Article
Pages 23-37
J. Bang-Jensen
The Fascination of Minimal Graphs Original Research Article
Pages 39-51
R. Bodendiek, K. Wagner
Optimal Paths and Cycles in Weighted Graphs Original Research Article
Pages 53-69
J.A. Bondy, G. Fan
A Note on Hamiltonian Graphs Original Research Article
Pages 71-74
H.J. Broersma
Uniqueness of the Biggs-Smith Graph Original Research Article
Pages 75-78
A.E. Brouwer
Some Complete Bipartite Graph—Tree Ramsey Numbers Original Research Article
Pages 79-89
S. Burr, P. Erdös, R.J. Faudree, C.C. Rousseau, R.H. Schelp
The Edge-Chromatic Class of Graphs with Maximum Degree at Least |V| – 3 Original Research Article
Pages 91-110
A.G. Chetwynd, A.J.W. Hilton
On Some Aspects of my Work with Gabriel Dirac Original Research Article
Pages 111-116
P. Erdös
Bandwidth versus Bandsize Original Research Article
Pages 117-129
P. Erdös, P. Hell, P. Winkler
Circumference and Hamiltonism in K1,33–Free Graphs Original Research Article
Pages 131-140
E. Flandrin, I. Fournier, A. Germa
The Prism of a 2–Connected, Planar, Cubic Graph is Hamiltonian (A Proof Independent of the Four Colour Theorem) Original Research Article
Pages 141-170
H. Fleischner
A Note Concerning some Conjectures on Cyclically 4–Edge Connected 3–Regular Graphs Original Research Article
Pages 171-177
H. Fleischner, B. Jackson
On Connectivity Properties of Eulerian Digraphs Original Research Article
Pages 179-194
A. Frank
Some Problems and Results on Infinite Graphs Original Research Article
Pages 195-210
R. Halin
On a Problem Concerning Longest Circuits in Polyhedral Graphs Original Research Article
Pages 211-219
J. Harant, H. Walther
Interpolation Theorems for the Independence and Domination Numbers of Spanning Trees Original Research Article
Pages 221-227
F. Harary, S. Schuster
Ein zum Vierfarbensatz Äquivalenter Satz der Panisochromie Original Research Article
Pages 229-253
H. Heesch
The Existence Problem for Graph Homomorphisms Original Research Article
Pages 255-265
P. Hell, J. Nešetřil
On Edge-Colorings of Cubic Graphs and a Formula of Roger Penrose Original Research Article
Pages 267-279
F. Jaeger
Longest ab-Paths in Regular Graphs Original Research Article
Pages 281-298
H.A. Jung
On Independent Circuits in Finite Graphs and a Conjecture of Erdös and Pósa. Original Research Article
Pages 299-305
P. Justesen
Contractions to Complete Graphs Original Research Article
Pages 307-310
L.K. Jørgensen
Triangulated Graphs with Marked Vertices Original Research Article
Pages 311-324
H.-G. Leimer
On a Problem upon Configurations Contained in Graphs with Given Chromatic Number Original Research Article
Pages 325-331
F. Lescure, H. Meyniel
On Disjoint Paths in Graphs Original Research Article
Pages 333-340
W. Mader
Conjecture de Hadwiger: Un Graphe k-Chromatique Contraction-Critique n'est pas k-Régulier Original Research Article
Pages 341-345
J. Mayer
A Theorem on Matchings in the Plane Original Research Article
Pages 347-354
M.D. Plummer
Removing Monotone Cycles from Orientations Original Research Article
Pages 355-362
O.R.L. Pretzel
Disentangling Pairings in Trees Original Research Article
Pages 363-369
G. Sabidussi
Colour-Critical Graphs with Vertices of Low Valency Original Research Article
Pages 371-396
H. Sachs, M. Stiebitz
About the Chromatic Number of 1-Embeddable Graphs Original Research Article
Pages 397-400
H. Schumacher
Problems and Conjectures in the Combinatorial Theory of Ordered Sets Original Research Article
Pages 401-416
W.T. Trotter
A Proof of Kuratowski's Theorem Original Research Article
Pages 417-419
H. Tverberg
Finite and Infinite Graphs whose Spanning Trees are Pairwise Isomorphic Original Research Article
Pages 421-435
P.D. Vestergaard
Bridges of Longest Circuits Applied to the Circumference of Regular Graphs Original Research Article
Pages 437-452
H.-J. Voss
On a Standard Method Concerning Embeddings of Graphs Original Research Article
Pages 453-472
K. Wagner, R. Bodendiek
Construction of Critical Graphs by Replacing Edges Original Research Article
Pages 473-485
W. Wessel
A Brief History of Hamiltonian Graphs Original Research Article
Pages 487-496
R.J. Wilson
Erinnerungen an Gabriel Dirac in Hamburg Original Research Article
Pages 497-498
E. Witt
Hamilton Paths in Multipartite Oriented Graphs Original Research Article
Pages 499-514
C.-Q. Zhang
Problems
Pages 515-517
