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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
