VERTEX PANCYCLICITY IN ALMOST REGULAR MULTIPARTITE TOURNAMENTS
Linqiang Pan · Chinese Annals of Mathematics,series A · 2002
Let T be a multipartite tournament and i(T) = max |d+(x) - d-(y)| (where x = yis admissible). T is said to be regular if i(T) = 0 and to be almost regular if i(T) ≤ 1. Volkmann conjectured in a survey paper that an almost regular c-partite tournament with c ≥ 4 is pancyclic. In this paper, it is snown that all almost regular c-pattite tournaments with c ≥ 5 are vertex pancyclic except for finite number of almost regular multipartite tournaments. The authors give an example to show that this conjecture does not hold whenc=4.