Table Of ContentLecture Notes in
Mathematics
Edited by A. Dold and B. Eckmann
642
Theory and Applications of Graphs
Proceedings, Michigan May 11-15,1976
Edited by
Y. Alavi and D. R. Lick
Springer-Verlag
Berlin Heidelberg New York 1978
Editors
Yousef Alavi
Don R. Lick
Department of Mathematics
Western Michigan University
Kalamazoo, MI 49008/USA
AMS Subject Classifications (1970): 05CXX, 94A20
ISBN 3-540-08666-8 Springer-Verlag Berlin Heidelberg New York
ISBN 0-387-08666-8 Springer-Verlag New York Heidelberg Berlin
This work is subject to copyright. All rights are reserved, whether the whole
or part of the material is concerned, specifically those of translation, re
printing, re-use of illustrations, broadcasting, reproduction by photocopying
machine or similar means, and storage in data banks. Under § 54 of the
German Copyright Law where copies are made for other than private use,
a fee is payable to the publisher, the amount of the fee to be determined by
agreement with the publisher.
© by Springer-Verlag Berlin Heidelberg 1978
Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr.
214113140-643210
DEDICATED TO THE
MEMORY OF
D. R. Fulkerson
Fernando Escalante
PREFACE
This volume constitutes the proceedings of the
International Conference on the Theory and Applications
of Graphs, held at Western Michigan University in
Kalamazoo, May 11-15, in the year of the Bicentennial
of the American Independence, Nineteen Hundred Seventy
six. Conference participants included research mathe
maticians from Colleges, Universities, and Industry,
as well as graduate and undergraduate students. In all
27 states and eight countries were represented. The con
tributions to this Volume* include a great variety of
topics in current research in both the theory and applica
tions of graphs, as well as a special Bicentennial histori
cal sketch, as the lead article, which is based on
Professor Robin Wilson's Banquet presentation.
*J. Bosak was unable to present his paper at the
Conference, but his contribution is included as part
of the published record.
ACKNOWLEDGEMENTS
For their generous contributions to the success of the Inter
national Conference and the preparation of these proceedings, the
editors gratefully acknowledge
The financial support of Western Michigan University;
The financial support of U. S. Army Research Office
Durham;
The overall support of the Department of Mathematics
and Professor A. Bruce Clarke, Chairman;
The assistance of the WMU Office of Research Services;
The outstanding contributions of our Co-Directors
of the Conference, Professors:
Gary Chartrand
S. F. Kapoor
Mark Jungerman
Arthur T. White
The fine administrative assistance of Mrs. Darlene Lard;
The excellent work of our Conference Assistant
Directors:
James M. Benedict Brian Garman
John F. Fink Ronald Gould
Annette Friedhoff Joseph Straight
The dedicated work of our team of Conference Assistants:
Vithal N. Bhave Marie Smith
Nancy Boynton Susan Steffens
David Burns Sui-Lung Tang;
The general and Secretarial assistance of Stacy George,
Darlene Lard, and Margo Johnson.
And, most definitely
the outstanding work of Mrs. Margo Johnson for her skill
ful typing of the manuscripts as well as her fine
assistance in numerous chores.
Y.A.
D.R.L.
LIST OF THE PARTICIPANTS IN
THE INTERNATIONAL CONFERENCE
ON THE
THEORY AND APPLICATIONS OF GRAPHS
Yousef Alavi * v. Chvatal
Michael Albertson E. J. Cockayne
David K. Baxter L. J. Cummings
Pierre Bayle Anastasia Czerniakiewicz
Thomas Beasley William H. E. Day
Mehdi Behzad Richard T. Denman
Lowell Beineke John K. Doyle
James Benedict ** Richard A. Duke
Claude Berge Roger B. Eggleton
David M. Berman Thomas Eitner
Arthur Bernhart Vance Faber
Frank R. Bernhart Ralph Faudree
vithal Bhave *** John Fink **
N. L. Biggs J. Sutherland Frame
Gary S. Bloom Annette Friedhoff **
Paul T. Boggs Marianne L. Gardner
Bela Bollobas Brian L. Garman **
Juraj Bosak Cyril W. L. Garner
Andre Bouchet Henry Glover
Nancy Boynton *** Donald Goldsmith
David Burns *** Martin Golumbic
Michael Capobianco Ronald Gould **
Paul A. Catlin R. L. Graham
Gary Chartrand * Donald L. Greenwell
Chang-Yun Chao Charles M. Grinstead
Phyllis Chinn Jonathan L. Gross
VIII
Ram P. Gupta John Mitchem
Gary Haggard John C. Molluzzo
S. Louis Hakimi J. W. Moon
Frank Harary V. Kumar Murty
Jehuda Hartman Ladislav Nebesky
Clare Heidema Edward A. Nordhaus
Arthur M. Hobbs Phillip Ostrand
Derek A. Holton Edgar M. Palmer
Charlotte Huang Torrence D. Parsons
Joan P. Hutchinson Raymond E. Pippert
Derbiau Hsu Albert D. Polimeni
Judy Johnson Geert Prins
Mark Jungerman * Louis V. Quintas
Paul Kainen K. Brooks Reid
S. F. Kapoor * Bruce Richmond
John W. Kennedy Richard D. Ringeisen
Hudson Kronk Gerhard Ringel
John LeFever Fred Roberts
Rochelle Leibowitz John Roberts
Linda M. Lesniak-Foster Neil Robertson
Hank Levinson Michael Rolle
Roy B. Levow David Roselle
Don R. Lick * Richard H. Schelp
Judith Q. Longyear Seymour Schuster
Paul J. McCarthy Allen J. Schwenk
Joseph Malkevitch Herbert Shank
Ben Manvel Gustavus J. Simmons
David Matula William Simpson
John S. Maybee Marie Smith ***
Zevi Miller Saul Stahl
IX
Susan Steffens ***
M. James Stewart
Paul K. Stockmeyer
Joseph Straight **
David Sumner
Siu-Lung Tang ***
J. Dalton Tarwater
Carsten Thomassen
William T. Trotter, Jr.
Alan Tucker
William T. Tutte
Donald W. Vanderjagt
Paul Vincent
Curtiss E. Wall
Mark E. Watkins
Arthur T. White *
E. G. Whitehead, Jr.
Susan Whitesides
Eva Williams
James williamson
Robin J. Wilson
D. R. Woodall
Daniel Younger
Conference - Co-Director *
Conference - Assistant Director **
Conference - Assistant ***
TABLE OF CONTENTS·
BANQUET ADDRESS - ROBIN J. WILSON
200 Years of Graph Theory . • 1
L. BABAI
Chromatic Number and Subgraphs of cayley Graphs 10
C. BERGE
The Multicolorings of Graphs and Hypergraphs. 23
F. R. BERNHART
Irreducible Configurations and the Four
Color Conjecture • . . • • . • • • • . 37
G. S. BLOOM AND S. W. GOLOMB
Numbered Complete Graphs, Unusual Rulers, and
Assorted Applications • . • • • • • . • • 53
B. BOLLOBAS
Cycles and Semi-Topological Configurations. 66
J. BOSAK
Graphs with Unique Walks, Trails or Paths
of Given Lengths •.•. . • • • . 75
A. BOUCHET
Triangular Imbeddings into Surfaces of a Join of
Equicardinal Independent Sets Following an Eulerian
Graph . • • • . . • • • . . . . . • . • • • • • • • 86
M. F. CAPOBIANCO AND J. MOLLUZZO
Mixed Graphs of Homomorphisms • • • • • • . • • • • • • 116
C-Y. CHAO AND E. G. WHITEHEAD, JR.
On Chromatic Equivalence of Graphs ••••••••••• 121
P. CHINN AND J. M. BENEDICT
On Graphs Having Prescribed Clique Number,
Chromatic Number, and Maximum Degree .••••••••• 132
E. J. COCKAYNE
Domination of Undirected Graphs - A Survey ••••••• 141
R. A. DUKE
Some Extremal Problems for Simple Two-Complexes • • • • 148
R. J. FAUDREE AND R. H. SCHELP
Various Length Paths in Graphs •••••••••.••• 160
J. S. FRAME
Orthogonal Groups over GF(2) and Related Graphs •••• 174
• On joint papers the speaker's name is listed first.
XII
R. L. GRAHAM AND L. LOV1i.SZ
Distance Matrix Polynomials of Trees • • • • • • • • • 186
D. GREENWELL
Odd Cycles and Perfect Graphs •.••••••••••• 191
J. L. GROSS
Imbeddings of Metacyclic Cayley Graphs • • • • • • • • 194
R. P. GUPTA
On the Chromatic Index and the Cover Index
of a Multigraph • • • • • • 204
G. HAGGARD
Pruning and Depth First Search . • • 216
S. L. HAKIMI AND E. F. SCHMEICHEL
Graphs and Their Degree Sequences: A Survey ••••. 225
F. HARARY
The Bichromaticity of a Tree ••. • 236
J. HARTMAN AND I. RUBIN
On Diameter Stability of Graphs ••• • 247
C. E. HEIDEMA
Generalized Pseudosurface Embeddings of. Graphs and
Associated Block Designs . . • . • • • . • 255
A. M. HOBBS
Powers of Graphs, Line Graphs, and Total Graphs. • 271
D. A. HOLTON AND J. SIMS
The Cartesian Product of Two Graphs is Stable ••••• 286
J. P. HUTCHINSON AND S. H. WHITESIDES
A Note on a Generalized Regularity Condition ••••• 304
P. C. KAINEN
Long and Short Walks in Trees • 309
J. W. KENNEDY
Random Clumps, Graphs, and Polymer Solutions • • • • • 314
L. M. LESNIAK, A. D. POLIMENI AND DONALD W. VANDERJAGT
Mixed Ramsey Numbers: Edge Chromatic
Numbers V.s. Graphs •••••.• • • • 330
H. W. LEVINSON
Planar and Outerplanar Cayley Graphs of
Free Groups . • • • • . • • • • • • • 342
R. B. LEVOW
Coloring Restrictions ••••••••••••••••• 347
J. Q. LONGYEAR
If a Hadamard Matrix of Order 24 has Character
exactly 2, its Transpose is known. • • • • • • • • • • 353
