An equivalent formulation of the Fan-Raspaud Conjecture and related problems

Authors

DOI:

https://doi.org/10.26493/1855-3974.1860.a3d

Keywords:

Cubic graph, perfect matching, oddness, Fan-Raspaud Conjecture, Berge-Fulkerson Conjecture, Petersen-colouring

Abstract

In 1994, it was conjectured by Fan and Raspaud that every simple bridgeless cubic graph has three perfect matchings whose intersection is empty. In this paper we answer a question recently proposed by Mkrtchyan and Vardanyan, by giving an equivalent formulation of the Fan-Raspaud Conjecture. We also study a possibly weaker conjecture originally proposed by the first author, which states that in every simple bridgeless cubic graph there exist two perfect matchings such that the complement of their union is a bipartite graph. Here, we show that this conjecture can be equivalently stated using a variant of Petersen-colourings, we prove it for graphs having oddness at most four and we give a natural extension to bridgeless cubic multigraphs and to certain cubic graphs having bridges.

Author Biography

Giuseppe Mazzuoccolo, University of Verona

Associate Professor, Department Computer Science

Published

2020-07-07

Issue

Section

Articles