29 research outputs found
On Fulkerson conjecture
If is a bridgeless cubic graph, Fulkerson conjectured that we can find 6
perfect matchings (a{\em Fulkerson covering}) with the property that every edge
of is contained in exactly two of them. A consequence of the Fulkerson
conjecture would be that every bridgeless cubic graph has 3 perfect matchings
with empty intersection (this problem is known as the Fan Raspaud Conjecture).
A {\em FR-triple} is a set of 3 such perfect matchings. We show here how to
derive a Fulkerson covering from two FR-triples. Moreover, we give a simple
proof that the Fulkerson conjecture holds true for some classes of well known
snarks.Comment: Accepted for publication in Discussiones Mathematicae Graph Theory;
Discussiones Mathematicae Graph Theory (2010) xxx-yy