Cycles of Each Length in Regular Tournaments

Brian Alspach

doi:10.4153/CMB-1967-028-6

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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.

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

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