Complementary cycles in regular multipartite tournaments, where one cycle has length five

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 Cycles Containing a Given Arc in Regular Multipartite Tournaments

In this paper we prove that if T is a regular n-partite tournament with n ≥ 4, then each arc of T lies on a cycle whose vertices are from exactly k partite sets for k = 4, 5, . . . , n. Our result, in a sense, generalizes a theorem due to Alspach.

Cycles through a given arc in almost regular multipartite tournaments

If x is a vertex of a digraph D, then we denote by d(x) and d−(x) the outdegree and the indegree of x, respectively. The global irregularity of a digraph D is defined by ig(D) = max{d+(x), d−(x)}−min{d+(y), d−(y)} over all vertices x and y of D (including x = y). If ig(D) = 0, then D is regular and if ig(D) ≤ 1, then D is almost regular. A c-partite tournament is an orientation of a complete c-...

Cycles Containing a Given Arc in Regular Multipartite Tournaments

In this paper we prove that if T is a regular n-partite tournament with n≥6, then each arc of T lies on a k-cycle for k=4,5,···,n. Our result generalizes theorems due to Alspach and Guo respectively.