Abstract
As a common generalization of matchings and matroid intersection, Cunningham and Geelen introduced the notion of path-matchings in 1996. Let K <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1,t</sub> denote the star with t + 1 vertices. A graph is K <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1. t</sub> -free if G contains no K <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1, t</sub> , as its induced subgraph. Sumner showed that (t - 1)-connected K <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1, t</sub> -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 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1, t</sub> -free graphs are presented. As an immediate consequence, we improve Sumner's result.
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