Rees R.S. (ed.) Graphs, Matrices, and Designs

Издательство Marcel Dekker, 1993, -322 pp.It is customary in mathematics to show one's love and respect for a senior colleague by dedicating a research paper to him or herbirthdays and special anniversaries are two usual occasions. This is a book containing 21 such research papers in honor of the sixtieth birthday of Professor Norman J. Pullman on March 31, 1991.
Professor Pullman, who hails from New York, obtained his Ph.D. at Syracuse University in 1962. He taught for three years at McGill University before taking up a postdoctoral fellowship at the University of Alberta in 1965. Since then he has been on the faculty of Queen's University, Kingston, Ontario, where he was promoted to Professor in 1971. In addition to being his sixtieth birthday, 1991 also marks his 25th year of service at Queen's. In this time Professor Pullman has supervised 13 graduate students, three of whom are represented in this collection (D. de Caen, W. Jackson, and R. Rees). He has been an Invited Lecturer at six different professional meetings over the last 12 years, including annual meetings of the AMS.
Professor Pullman has a long-standing association with Curtin University of Technology (formerly Western Australian Institute of Technology), Perth, Australia. He has been a Visiting Scholar there on several occasions in the last ten years.
Professor Pullman's research has spanned a wide range of topics in matrix theory, linear algebra, and graph theory. He has made significant contributions to the theory of tournaments and tournament matrices, the study of clique and biclique covering numbers and their relation to the problem of determining the Boolean and real ranks of binary matrices, and the study of linear operators that preserve some prescribed property of a matrix (over some semiring). The 21 excellent chapters in this volume cover many aspects of his interests and constitute a representative sampler of current research in these areas. As such, we expect that this book will be of interest to anyone working in one or more of these areas.
To those who are familiar with Professor Pullman's work, the inclusion of design theory as one of his interests may at first seem to be something of a curiosity. Keeping in mind, however, that a pairwise balanced design is just an edge-clique partition of the complete graph, one of Professor Pullman's favorite problems (that of determining the clique partition number of the graph K_v\K_k) is very closely related to a well-known extremal problem in design theory (that of determining the smallest number g(^k)(v) of blocks required to construct a pairwise balanced design on v points in which the largest block has size k)
Norman J. Pullman's Publications to April 1992.
Around a Formula for the Rank of a Matrix Product with Some Statistical Applications.
Linear Operators Preserving Partition Numbers of Graphs.
Faithful Enclosing of Triple Systems: A Generalization of Stern's Theorem.
Completion of the Spectrum of Orthogonal Diagonal Latin Squares.
Deficiencies and Vertex Clique Covering Numbers of Cubic Graphs.
Extremal Problems for the Bondy-Chvatal Closure of a Graph.
The 3-Hypergraphical Steiner Quadruple Systems of Order Twenty.
Minimum Biclique Partitions of the Complete Multigraph and Related Designs.
Multiplicativity of Generalized Permanents over Semirings.
A Few More Room Frames.
Pairwise Balanced Designs with Block Sizes 5t+1.
Pairwise Balanced Designs with Holes.
The Sum Number of Complete Bipartite Graphs.
Biclique Covers and Partitions of Unipathic Digraphs.
Maximal Partial Latin Squares.
Longest Cycles in 3-Connected Graphs of Bounded Maximum Degree.
Construction of New Hadamard Matrices with Maximal Excess and Infinitely Many New SBIBD (4k2,2k2+k, k2+k).
Maximum Order Digraphs for Diameter 2 or Degree 2.
Minimal Clique Partitions of Norm Three II.
The Cycle Space of an Embedded Graph III.
Pseudo-One-Factorizations of Regular Graphs of Odd Order I: Some General Questions.