Petersen Coloring Conjecture

Prove that every bridgeless cubic graph admits a Petersen-graph coloring; equivalently, for every bridgeless cubic graph G, there exists a proper edge-coloring f:E(G)\to E(P) such that at each vertex of G the images of its incident edges form the set of edges incident with some vertex of the Petersen graph P.

Background

The paper introduces the Petersen Coloring Conjecture as a central unresolved problem concerning bridgeless cubic graphs. A graph H colors a graph G when there is a proper edge mapping from E(G) to E(H) that maps the edge set incident with every vertex of G onto the edge set incident with some vertex of H. The conjecture asserts that the Petersen graph provides such a coloring for every bridgeless cubic graph.

The conjecture is significant because, if true, it would imply other longstanding results and conjectures, including the Berge–Fulkerson Conjecture and the 5-Cycle Double Cover Conjecture. The paper notes that although the conjecture has been verified computationally for all bridgeless cubic graphs of order at most 36, a general resolution remains out of reach. Unlike the S10- and S12-Conjectures, which the paper disproves, the Petersen Coloring Conjecture is not resolved here.