Geodesic
Perfect matchings in claw-free cubic graphs
The electronic journal of combinatorics, Tome 18 (2011) no. 1
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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.
DOI : 10.37236/549
Classification : 05C70, 05C38
Mots-clés : perfect matching, claw free graph, cubic graph 
@article{10_37236_549,
     author = {Sang-il Oum},
     title = {Perfect matchings in claw-free cubic graphs},
     journal = {The electronic journal of combinatorics},
     year = {2011},
     volume = {18},
     number = {1},
     doi = {10.37236/549},
     zbl = {1217.05188},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/549/}
}
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Sang-il Oum. Perfect matchings in claw-free cubic graphs. The electronic journal of combinatorics, Tome 18 (2011) no. 1. doi: 10.37236/549

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