关于图的分数横贯的一个注记

A note on fractronal transversals of graphs

对于一个超图H,有等式maxs≥1υs(H)s=υ (H)=τ (H)=mink≥1τk(H)k.若H是简单图G,用纯图论的方法证明了τ (G)=τ2(G)2=υ2(G)2,现用线性代数的方法证明这一等式成立.用这一方法有希望刻划出对于r 一致超图H来说达到最大、最小值所对应的s及k.

Every hypergraph H satisfies the following equality: \{max\}s≥1υ\-s(H)s=υ\+*(H)=τ\+*(H)=\{\{min\}k≥1τ\-k(H)k\}.If H is a simple graph G, then G satisfies the equality:τ\+*(G)=τ\-2(G)2=υ\-2(G)2. This equality was proved by pure graph method. This paper proved it by linear algebra method. Using this method, it is possible to characterize the numbers s and k when they achieve the maximun or the minimun for runiform hypergraph.