完全偶图的DS-因子计数

The Enumeration of DS-factors of Complete Bipartite Graph

一个图H称为一个双星(Doub le Star),当H由2个不交的星K1,m1,K1,m2加上连接它们最大度点的一条边所构成.图G的一个支撑子图F称为一个双星(DS)因子,当F的每一个连通分支是一个双星.本文研究完全偶图Km,n的DS-因子计数,给出了Km,n的DS-因子计数公式.

A graph H can he called a double star （DS） if H consists of two disjoint stars K1. m1, K1. m2, together with an edge between a vertex in K1. m1 and a vertex in K1,m2 which have the maximum degrees in K1,m1 and K1,m2 respectively. A spanning subgraph F of a graph G can he a DS-factor when every connected component of F is a DS. This paper presents the formula of enumeration of DS-factors of a complete bipartite graph.