Petersen coloring conjecture

Statement

An Eulerian subgraph of a graph $G$ is a subgraph consisting of a subset of the edges of $G$, touching every vertex of $G$ an even number of times. These subgraphs are the elements of the cycle space of $G$ and are sometimes called cycles. If $G$ and $H$ are any two graphs, a function from the edges of $G$ to the edges of $H$ is defined to be cycle-continuous if the pre-image of every cycle of $H$ is a cycle of $G$. A conjecture of Jaeger asserts that every bridgeless graph has a cycle-continuous mapping to the Petersen graph. Jaeger showed this conjecture implies the 5-cycle-double-cover conjecture and the Berge-Fulkerson conjecture."