Designs and Graphs: Volume 4(Volume 4 Topics in Discrete Mathematics)

In 1988, the news of Egmont Köhler's untimely death at the age of 55 reached his friends and colleagues. It was widely felt that a lasting memorial tribute should be organized. The result is the present volume, containing forty-two articles, mostly in combinatorial design theory and graph theory, and all in memory of Egmont Köhler. Designs and graphs were his areas of particular interest; he will long be remembered for his research on cyclic designs, Skolem sequences, t-designs and the Oberwolfach problem. Professors Lenz and Ringel give a detailed appreciation of Köhler's research in the first article of this volume.There is, however, one aspect of Egmont Köhler's biography that merits special attention. Before taking up the study of mathematics at the age of 31, he had completed training as a musician (studying both composition and violoncello at the Musikhochschule in Berlin), and worked as a cellist in a symphony orchestra for some years. This accounts for his interest in the combinatorial aspects of music. His work and lectures in this direction had begun to attract the interest of many musicians, and he had commenced work on a book on mathematical aspects of musical theory. It is tragic indeed that his early death prevented the completion of his work; the surviving paper on the classification and complexity of chords indicates the loss that his death meant to the area, as he was almost uniquely qualified to bring mathematics and music together, being a professional in both fields.

Table of Contents:
A Brief Review on Egmont Köhler's Mathematical Work. Edge-pancyclic Block-intersection Graphs. Symmetric Divisible Designs with k - &lgr;1 = 1. Some Constructions of Group Divisible Designs with Singer Groups. On Indecomposable Pure Mendelsohn Triple Systems. A Combinatorial Characterization of Geometric Spreads. Hermitian Unitals are Code Words. Long Cycles in Subgraphs with Prescribed Minimum Degree. Covers of Graphs and EGQs. The 2-rotational Steiner Triple Systems of Order 25. Outline Symmetric Latin Squares. Intersections and Supports of Quadruple Systems. Directed Star Decompositions of Directed Multigraphs. Some Naive Constructions of S(2,3,v) and S(2,4,v). On the Maximum Cardinality of Binary Constant Weight Codes with Prescribed Distance. Über einen Satz von Köhler. Mutually Balanced Nested Designs. Difference Families from Rings. Transitive Multipermutation Graphs. On Infinite Steiner Systems. Tree-partitions of Infinite Graphs. Plane Four-regular Graphs with Vertex-to-vertex Unit Triangles. Simple Direct Constructions for Hybrid Triple Designs. Sets in a Finite Plane with Few Intersection Numbers and a Distinguished Point. The Existence of Ck-factorizations of K2n - F. Self-orthogonal Hamilton Path Decompositions. Cyclic 2-(91,6,1) Designs with Multiplier Automorphisms. The Spectrum of &agr;-resolvable Block Designs With Block Size 3. On Near Generalized Balanced Tournament Designs. On Parallelism in Steiner Systems. Skolem Labelled Graphs. On the Simplicity of ˙2 and ˙3. A Class of 2-Chromatic SQS(22). The Solution of the Bipartite Analogue of the Oberwolfach Problem. The Spectrum of Maximal Sets of One-factors. A Note on Check Character Systems Using Latin Squares. On the Existence of Cyclic Steiner Quadruple Systems SQS(2p). Designs Constructed from Maximal Arcs. On the Chromatic Number of Special Distance Graphs. About Special Classes of Steiner Systems S(2,4,v). A Few More RBIBDs with k=5 and &lgr;=1. Research Problems.