Mácajová and Škoviera Conjecture on Cubic Graphs (0809.4839v2)

Abstract: A conjecture of M\'a\u{c}ajov\'a and \u{S}koviera asserts that every bridgeless cubic graph has two perfect matchings whose intersection does not contain any odd edge cut. We prove this conjecture for graphs with few vertices and we give a stronger result for traceable graphs.