Pancyclic in-tournaments Original Research Article

An in-tournament is an oriented graph, where the negative neighborhood of every vertex induces a tournament. In this paper, the influence of the minimum indegree δ−(D) of an in-tournament D on its k-pancyclicity is considered. An oriented graph of order n is said to be k-pancyclic for some 3⩽k⩽n, if it contains an oriented cycle of length t for every k⩽t⩽n. For every 3⩽k⩽n, a lower bound for δ−(D) is presented that ensures a strong in-tournament to be k-pancyclic. Examples show that all bounds given here are best possible.