Let G be a bridgeless cubic graph. Fulkerson conjectured that there exist six 1-factors of G such that each edge of G is contained in exactly two of them. Berge conjectured that the edge-set of G can becovered with at most five 1-factors. We prove that the two conjectures are equivalent.
The equivalence of two conjectures of Berge and Fulkerson / Mazzuoccolo, Giuseppe. - In: JOURNAL OF GRAPH THEORY. - ISSN 1097-0118. - STAMPA. - 68:(2011), pp. 125-128. [10.1002/jgt.20545]
The equivalence of two conjectures of Berge and Fulkerson
MAZZUOCCOLO, Giuseppe
2011
Abstract
Let G be a bridgeless cubic graph. Fulkerson conjectured that there exist six 1-factors of G such that each edge of G is contained in exactly two of them. Berge conjectured that the edge-set of G can becovered with at most five 1-factors. We prove that the two conjectures are equivalent.
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