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Cycles of Each Length in Regular Tournaments

Published online by Cambridge University Press:  20 November 2018

Brian Alspach
Brian Alspach*
Affiliation:
Simon Fraser University
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It is known that a strong tournament of order n contains a cycle of each length k, k=3,…, n, ([l], Thm. 7). Moon [2] observed that each vertex in a strong tournament of order n is contained in a cycle of each length k, k = 3,…, n. In this paper we obtain a similar result for each arc of a regular tournament, that is, a tournament in which all vertices have the same score.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 10 , Issue 2 , June 1967 , pp. 283 - 286
Copyright
Copyright © Canadian Mathematical Society 1967

References

1. Harary, F. and Moser, L., The theory of round robin tournaments. Amer. Math. Monthly, 73 (1966), 231-246.Google Scholar
2. Moon, J. W., On sub tournaments of a tournament. Canad. Math. Bull., 9 (1966), 297-301.Google Scholar