关于图的星形因子覆盖

ON STAR FACTOR COVERED GRAPHS

如果图 G 的支撑子图 M 的每个分支都同构于{K_(1,1)K_(1,2,)…,K_(1,k}(k≥2)中的某个 K_(1,i),则 M(?)叫做 G 的星形因子。进一步,如果对于图 G 的每一条边都存在一个星形因子包含这条边,则称图 G 是星形因子覆盖的。本文给出了图是{P_2,P_3}一因子覆盖的充要条件,并证明了任意正则图均存在星形因子覆盖。

A star—factor of a graph G is defined to be a spanning subgraph of Geach component of which is isomorphic to one of {K_(1,1),K_(1,2),…,K_(i,k)}(k≥2).A graph G is star—factor covered if every edge of G belongs to a star-factor.In this paper,we give a criterion for graphs to be {P_2,P_3}-factor-cov ered.We also show that every regular graph is star-factor covered,