On the existence of specified cycles in bipartite tournaments

Two-Path Convexity and Bipartite Tournaments of Small Rank

We study two-path convexity in bipartite tournaments. For a bipartite tournament, we obtain both a necessary condition and a sufficient condition on the adjacency matrix for its rank to be two. We then investigate 4-cycles in bipartite tournaments of small rank. We show that every vertex in a bipartite tournament of rank two lies on a four cycle, and bipartite tournaments with a maximum number ...

Complementary cycles containing a fixed arc in diregular bipartite tournaments

Let (x, y) be a specified arc in a k-regular bipartite tournament B. We prove that there exists a cycle C of length four through (x, y) in B such that B-C is hamiltonian.

A sufficient condition for Hamilton cycles in bipartite tournaments

Determining properties of a multipartite tournament from its lattice of convex subsets

The collection of convex subsets of a multipartite tournament T forms a lattice C(T ). Given a lattice structure for C(T ), we deduce properties of T . In particular, we find conditions under which we can detect clones in T . We also determine conditions on the lattice which will imply that T is bipartite, except for a few cases. We classify the ambiguous cases. Finally, we study a property of ...

On (1, 2)-step competition graphs of bipartite tournaments

In this paper, we study (1, 2)-step competition graphs of bipartite tournaments. A bipartite tournament means an orientation of a complete bipartite graph. We show that the (1, 2)-step competition graph of a bipartite tournament has at most one non-trivial component or consists of exactly two complete components of size at least three and, especially in the former, the diameter of the nontrivia...