3 research outputs found
Pancyclic arcs and connectivity in tournaments
A tournament is an orientation of the edges of a complete graph. An arc is pancyclic in a digraph D if it is contained in a cycle of length l, for every . In [4], Moon showed that every strong tournament contains at least three pancyclics arcs and characterized the tournaments with exactly three pancyclic arcs. All these tournaments are not 2-strong. In this paper, we are interested in the minimum number of pancyclic arcs in a k-strong tournament of order n. We conjecture that (for ) there exists a constant such that . After proving that every 2-strong tournament has a hamiltonian cycle containing at least five pancyclic arcs, we deduce that for , . We then characterize the tournaments having exactly four pancyclic arcs and those having exactly five pancyclic arcs