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arXiv · 0906.2261

Perfect Matchings in Claw-free Cubic Graphs

Sang-il Oum
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Abstract

Lovasz and Plummer conjectured that there exists a fixed positive constant c such that every cubic n-vertex graph with no cutedge has at least 2^(cn) perfect matchings. Their conjecture has been verified 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 2^(n/12) perfect matchings, thus verifying the conjecture for claw-free graphs.

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Sang-il Oum. 2009-11-09. Perfect Matchings in Claw-free Cubic Graphs. https://doi.org/10.37236/549

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