The average connectivity of regular multipartite tournaments

Two-path convexity in clone-free regular multipartite tournaments

We present some results on two-path convexity in clone-free regular multipartite tournaments. After proving a structural result for regular multipartite tournaments with convexly independent sets of a given size, we determine tight upper bounds for their size (called the rank) in clone-free regular bipartite and tripartite tournaments. We use this to determine tight upper bounds for the Helly a...

Almost all almost regular c-partite tournaments with cgeq5 are vertex pancyclic

A tournament is an orientation of a complete graph and a multipartite or c-partite tournament is an orientation of a complete c-partite graph. If D is a digraph, then let d + (x) be the outdgree and d ? (x) the indegree of the vertex x in D. The minimum (maximum) out-degree and the minimum (maximum) indegree of D are denoted by + ((+) and ? ((?), respectively. In addition, we deene = minf + ; ?...

Complementary cycles in regular multipartite tournaments

Weakly Complementary Cycles in 3-Connected Multipartite Tournaments

The vertex set of a digraph D is denoted by V (D). A c-partite tournament is an orientation of a complete c-partite graph. A digraph D is called cycle complementary if there exist two vertex disjoint cycles C1 and C2 such that V (D) = V (C1) ∪ V (C2), and a multipartite tournament D is called weakly cycle complementary if there exist two vertex disjoint cycles C1 and C2 such that V (C1) ∪ V (C2...

On two-path convexity in multipartite tournaments

In the context of two-path convexity, we study the rank, Helly number, Radon number, Caratheodory number, and hull number for multipartite tournaments. We show the maximum Caratheodory number of a multipartite tournament is 3. We then derive tight upper bounds for rank in both general multipartite tournaments and clone-free multipartite tournaments. We show that these same tight upper bounds ho...