In an in-cycle system C of order n the blocks are the vertex sets of n(n-1)/(2m) cycles C-i such that each edge of the complete graph K-n belongs to precisely one cycle C-i is an element of C. We prove the existence of m-cycle systems that admit no vertex partition into two classes in such a way that each class meets every cycle of C. The proofs apply both constructive and probabilistic methods, and also some old and new facts about Steiner Triple Systems without large independent sets. (C) 1996 John Wiley & Sons, Inc.

Cycle systems without 2-colorings

MILICI, Salvatore;
1996-01-01

Abstract

In an in-cycle system C of order n the blocks are the vertex sets of n(n-1)/(2m) cycles C-i such that each edge of the complete graph K-n belongs to precisely one cycle C-i is an element of C. We prove the existence of m-cycle systems that admit no vertex partition into two classes in such a way that each class meets every cycle of C. The proofs apply both constructive and probabilistic methods, and also some old and new facts about Steiner Triple Systems without large independent sets. (C) 1996 John Wiley & Sons, Inc.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11769/13869
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