Partitioning Vertices of a Tournament into Independent Cycles

This article will generally follow the notation and terminology defined in [1]. A digraph is called strongly connected or strong if for every pari of vertices u and v there exists a directed path from u to v and a directed path from v to u. Let k be a positive integer. A digraph G is k-connected if the removal of any set of fewer than k vertices results in a strong digraph. A tournament with n vertices will also be called an n-tournament. It is well-known that every tournament contains a hamiltonian path and every strong tournament contains a hamiltonian cycle. Reid [2] proved that if T is a 2-connected n-tournament, n 6, that is, T is not the 7-tournament that contains no transitive subtournament with 4 vertices (i.e., the quadratic residue 7-tournament), then T contains two vertex-disjoint cycles doi:10.1006 jctb.2001.2048, available online at http: www.idealibrary.com on