Petersen Graph - Petersen Coloring Conjecture

Petersen Coloring Conjecture

According to DeVos, Nesetril, and Raspaud, "A cycle of a graph G is a set C E(G) so that every vertex of the graph (V(G),C) has even degree. If G,H are graphs, we define a map φ: E(G) —> E(H) to be cycle-continuous if the pre-image of every cycle of H is a cycle of G. A fascinating conjecture of Jaeger asserts that every bridgeless graph has a cycle-continuous mapping to the Petersen graph. Jaeger showed that if this conjecture is true, then so is the 5-cycle-double-cover conjecture and the Berge-Fulkerson conjecture."