Perfect Matchings in Claw-free Cubic Graphs

Details Perfect Matchings in Claw-free Cubic Graphs Perfect Matchings in Claw-free Cubic Graphs

2009-06-12

arxiv.org/abs/0906.2261v2

Mathematics

Combinatorics

6 pages, 2 figures

Scientific paper

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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