Designs and Graphs

C.J. Colbourn, D. Jungnickel, A. Rosa

• Publisher: North Holland
• Year: 2016
• ISBN:
  9781483294759
• Topic: Mathematics
• Subtopic: Discrete Mathematics
• Index: Mathematics

In 1988, the news of Egmont Köhler's untimely death at the age of 55reached his friends and colleagues. It was widely felt that a lastingmemorial tribute should be organized. The result is the present volume, containing forty-two articles, mostly in combinatorial design theory andgraph theory, and all in memory of Egmont Köhler. Designs and graphswere his areas of particular interest; he will long be remembered for hisresearch on cyclic designs, Skolem sequences, t -designs and theOberwolfach problem. Professors Lenz and Ringel give a detailedappreciation of Köhler's research in the first article of thisvolume.

There is, however, one aspect of Egmont Köhler's biographythat merits special attention. Before taking up the study of mathematics atthe age of 31, he had completed training as a musician (studying bothcomposition and violoncello at the Musikhochschule in Berlin), and workedas a cellist in a symphony orchestra for some years. This accounts for hisinterest in the combinatorial aspects of music. His work and lectures inthis direction had begun to attract the interest of many musicians, and hehad commenced work on a book on mathematical aspects of musical theory. Itis tragic indeed that his early death prevented the completion of his work;the surviving paper on the classification and complexity of chordsindicates the loss that his death meant to the area, as he was almostuniquely qualified to bring mathematics and music together, being aprofessional in both fields.

Table of contents

• Front Cover
• Designs and Graphs
• Copyright Page
• Table of Contents
• Preface
• Chapter 1. A brief review on Egmont Köhler's mathematical work
• Chapter 2. Edge-pancyclic block-intersection graphs
• Chapter 3. Symmetric divisible designs with k —λ1 = 1
• Chapter 4. Some constructions of group divisible designs with Singer groups
• Chapter 5. On indecomposable pure Mendelsohn triple systems
• Chapter 6. A combinatorial characterization of geometric spreads
• Chapter 7. Hermitian unitals are code words
• Chapter 8. Long cycles in subgraphs with prescribed minimum degree
• Chapter 9. Covers of graphs and EGQs
• Chapter 10. The 2-rotational Steiner triple systems of order 25
• Chapter 11. Outline symmetric latin squares
• Chapter 12. Intersections and supports of quadruple systems
• Chapter 13. Directed star decompositions of directed multigraphs
• Chapter 14. Some naive constructions of S(2, 3, v) and S(2, 4, v)
• Chapter 15. On the maximum cardinality of binary constant weight codes with prescribed distance
• Chapter 16. Über einen Satz von Köhler
• Chapter 17. Mutually balanced nested designs
• Chapter 18. Difference families from rings
• Chapter 19. Transitive multipermutationgraphs: case 4 ≤ n ≤ m
• Chapter 20. On infinite Steiner systems
• Chapter 21. Tree-partitions of infinite graphs
• Chapter 22. Plane four-regular graphs with vertex-to-vertex unit triangles
• Chapter 23. Simple direct constructions for hybrid triple designs
• Chapter 24. Sets in a finite plane with few intersection numbers and a distinguished point
• Chapter 25. The existence of C^-factorizations of K2n — F
• Chapter 26. Self-orthogonal Hamilton path decompositions
• Chapter 27. Cyclic 2- (91, 6,1) designs with multiplier automorphisms
• Chapter 28. The spectrum of α-resolvable block designs with block size 3
• Chapter 29. On near generalized balanced tournament designs
• Chapter 30. On parallelism in Steiner systems
• Chapter 31. Skolem labelled graphs
• Chapter 32. On the simplicity of .2 and .3
• Chapter 33. A class of 2-chromatic SQS(22)
• Chapter 34. The solution of the bipartite analogue of the Oberwolfach problem
• Chapter 35. The spectrum of maximal sets of one-factors
• Chapter 36. A note on check character systems using Latin squares
• Chapter 37. On the existence of cyclic Steiner Quadruple Systems SQS(2p)
• Chapter 38. Designs constructed from maximal arcs
• Chapter 39. On the chromatic number of special distance graphs
• Chapter 40. About special classes of Steiner systems S(2, 4, v)
• Chapter 41. A few more RBIBDs with k = 5 and λ = 1
• Research problems
• Author index to volume 97 (1991)