Open Problem Garden

Importance: High ✭✭✭

Author(s):	Arthur
	Hoffmann-Ostenhof

Subject:	Graph Theory
	» Basic Graph Theory
	» » Cycles

Keywords:

cycle cover

Recomm. for undergrads: yes

Prize: 50 Euro

Posted	by:	arthur
	on:	August 3rd, 2010

Conjecture Let $C$ be a circuit in a bridgeless cubic graph $G$ . Then there is a five cycle double cover of $G$ such that $C$ is a subgraph of one of these five cycles.

A cycle in $G$ is meant to be a $2$ -regular subgraph of $G$ . A five cycle double cover of $G$ is a set of five cycles of $G$ such that every edge of $G$ is contained in exactly two of these cycles.