Perfect matchings with restricted intersection in cubic graphs

A conjecture of G. Fan and A. Raspaud asserts that every bridgeless cubic graph contains three perfect matchings with empty intersection. We suggest a possible approach to problems of this type, based on the concept of a balanced join in an embedded graph. We use this method to prove that bridgeless cubic graphs of oddness two have Fano colorings using only 5 lines of the Fano plane. This is a special case of a conjecture by E. M

• Type: Journal
• Year: 2010
• Where: EJC
• Authors: Tomás Kaiser, André Raspaud
• Keywords: Bridgeless Cubic Graphs, EJC 2007, EJC 2010, Perfect Matchings, Possible Approach