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Graph Theory » Basic G.T. » Matchings

Exponentially many perfect matchings in cubic graphs ★★★

Author(s): Lovasz; Plummer

Conjecture   There exists a fixed constant $ c $ so that every $ n $-vertex cubic graph without a cut-edge has at least $ e^{cn} $ perfect matchings.

Keywords: cubic; perfect matching

Posted by mdevos
updated December 15th, 2010
2 comments
Graph Theory » Basic G.T. » Matchings

The intersection of two perfect matchings ★★

Author(s): Macajova; Skoviera

Conjecture   Every bridgeless cubic graph has two perfect matchings $ M_1 $, $ M_2 $ so that $ M_1 \cap M_2 $ does not contain an odd edge-cut.

Keywords: cubic; nowhere-zero flow; perfect matching

Posted by mdevos
updated August 30th, 2007
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Graph Theory » Basic G.T. » Matchings

The Berge-Fulkerson conjecture ★★★★

Author(s): Berge; Fulkerson

Conjecture   If $ G $ is a bridgeless cubic graph, then there exist 6 perfect matchings $ M_1,\ldots,M_6 $ of $ G $ with the property that every edge of $ G $ is contained in exactly two of $ M_1,\ldots,M_6 $.

Keywords: cubic; perfect matching

Posted by mdevos
updated November 23rd, 2011
9 comments
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