Séminaire Lotharingien de Combinatoire, B47b (2001), 17 pp.

Andreas Dress, M. Klucznik, Jack Koolen and Vincent Moulton

2kn - Binomial(2k+1,2)

Abstract. It is shown that every cyclic split system S defined on an n-set with #S > 2kn - Binomial(2k+1, 2) for some k <= (n-1)/2 always contains a subset of k+1 pairwise incompatible splits provided one has min(k,n - (2k+1)) <= 3. In addition, some related old and new conjectures are also discussed.

Received: March 25, 2001; Revised: August 8, 2001; Accepted: November 12, 2001.

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