All 2-connected in-tournaments that are cycle complementary Original Research Article

An in-tournament is an oriented graph such that the negative neighborhood of every vertex induces a tournament. A digraph image is cycle complementary if there exist two vertex-disjoint directed cycles spanning the vertex set of image. Let image be a 2-connected in-tournament of order at least 8. In this paper we show that image is not cycle complementary if and only if it is 2-regular and has odd order.