On Fan Raspaud Conjecture

TL;DR

This paper investigates the Fan Raspaud Conjecture, proposing new results and establishing a lower bound of 32 vertices for any minimal counterexample in bridgeless cubic graphs.

Contribution

It provides new insights into the conjecture and proves a lower bound on the size of potential counterexamples.

Findings

Minimum counterexample has at least 32 vertices

New results concerning the Fan Raspaud Conjecture

Discussion on balanced joins in embedded graphs

Abstract

A conjecture of Fan and Raspaud [3] asserts that every bridgeless cubic graph con-tains three perfect matchings with empty intersection. Kaiser and Raspaud [6] sug-gested a possible approach to this problem based on the concept of a balanced join in an embedded graph. We give here some new results concerning this conjecture and prove that a minimum counterexample must have at least 32 vertices.