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Berge, Claude


Graph Theory » Coloring

Linial-Berge path partition duality ★★★

Author(s): Berge; Linial

Conjecture   The minimum $ k $-norm of a path partition on a directed graph $ D $ is no more than the maximal size of an induced $ k $-colorable subgraph.

Keywords: coloring; directed path; partition

Posted by berger
updated September 19th, 2007
2 comments
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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