Covering a 3-graph with perfect matchings

Details Covering a 3-graph with perfect matchings Covering a 3-graph with perfect matchings

2011-11-08

arxiv.org/abs/1111.1871v2

Mathematics

Combinatorics

submitted

Scientific paper

Let G be a bridgeless cubic graph. A well-known conjecture of Berge and Fulkerson can be stated as follows: there exist five perfect matchings of G such that each edge of G is contained in at least one of them. Here, we prove that in each bridgeless cubic graph there exist five perfect matchings covering a portion of the edges at least equal to 215/231 . Furthermore, we decrease the best known upper bound, expressed in terms of the size of the graph, for the number of perfect matchings needed to cover the edge-set of G.

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