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{\bf Sang-il Oum}
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{\bf Perfect Matchings in Claw-free Cubic Graphs}
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Lov\'asz 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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