竞赛图中给定长度的点不相交的圈

Vertex-disjoint cycles of prescribed length on tournaments

对Lichiardopol提出的猜想,给定正整数q≥3,r≥1,在竞赛图T中,若最小出度δ+(T)≥(q-1)r-1,则在T中至少存在r个点不相交的q圈.证明了当r≤3时,这个猜想的正确性.

Lichiardopol conjectures that for any given positive integers q ≥3 and r ≥1,any tournament T of the minimum out-degree at least(q-1) r-1 contains at least r vertex-disjoint q-cycles. We have proved that this conjecture is true in the special case when r≤3.