竞赛图满足dám猜想的一个充分条件

A Sufficient Condition for Tournaments to Satisfy dám's Conjecture

对于竞赛图G=(V,A),证明了如果存在一弧xy满足条件:(1)y到x有长度为2的路径;(2)x到y没有长度为2的路径,则反向弧xy后G中圈的个数减少,即G满足dám猜想.

For a tournament G=(V,A),it is proved that if there exists an arc xy which satisfy the conditions:(1) G has a path of length 2 from yto x;2) G has no path of length 2 from x to y,then the reversal of xy decreases the total number of cycles in G,i.e.G satisfies dám's conjecture.