Perfect Matchings in Claw-free Cubic Graphs

Sang-il Oum


Lovász 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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