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    Title      l  Perfect Matchings in Claw-free Cubic Graphs
    Author   l  Sang-il Oum
    Date   l  2009-09-21
    Category   l  ASARC-Preprint-09-27
    Download    l clawfree.pdf  
Abstract: Lovasz and Plummer conjectured that there exist a xed positive con-stant c such that every
cubic n-vertex graph with no cutedge has at least 2cn perfect matchings. Their conjecture has
been veried for bipartite graphs by Voorhoeve and planar graphs by Chudnovsky and Seymour.
We prove that every claw-free cubic n-vertex graph with no cutedge has more than 2n=18
perfect matchings, thus verifying the conjecture for claw-free graphs.

Keyword

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