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.