## Designs and graphsIn 1988, the news of Egmont Kouml;hler'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 Kouml;hler. 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 Kouml;hler's research in the first article of this volume.There is, however, one aspect of Egmont Kouml;hler'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. |

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### Contents

CONTENTS | 1 |

B Alspach and D Hare | 17 |

K T Arasu and A Pott | 39 |

Copyright | |

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1-factor 1990 In memory 2-rotational 3-row complementary abelian arcs automorphism group B.V. All rights base blocks cell Colbourn colour column Combinatorics complete graph construction contains Corollary cycle of length cyclic defined denote difference family Discrete Math Discrete Mathematics Discrete Mathematics 97 disjoint edges Egmont Kohler elements Elsevier Science Publishers exactly exists factor finitely attached graph G Graph Theory Hamilton path Hamilton path decomposition Hence Hermitian infinite integer intersection isomorphic Jungnickel Lemma maximal arcs memory of Egmont multigraph North-Holland obtain octad one-factors orbits orthogonal pair pairwise parameters partition pathlike factorisation points prime power Proof prove pseudo-tree pure MTS(u quasigroup Received 7 March result satisfying Science Publishers B.V. self-orthogonal Hamilton path Skolem labelled ssssss ssssss ssssss Steiner quadruple systems Steiner systems Steiner triple systems strongly regular graphs subset subsystems symbols symmetric latin square Theorem Theorem 2.1 vectors vertex vertices