Forbidden subgraph and perfect path-matchings

As a common generalization of matchings and matroid intersection, Cunningham and Geelen introduced the notion of path-matchings in 1996. Let K
_1,t
denote the star with t + 1 vertices. A graph is K
_{1. t}
-free if G contains no K
_{1, t}
, as its induced subgraph. Sumner showed that (t - 1)-connected K
_{1, t}
-free graphs with even number of vertices have a perfect matching. In this paper, some sufficient conditions for the existence of perfect path-matching of K
_{1, t}
-free graphs are presented. As an immediate consequence, we improve Sumner's result.