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Petersen coloring conjecture

An Eulerian subgraph of a graph G {\displaystyle G} is a subgraph consisting of a subset of the edges of G {\displaystyle G}, touching every vertex of G {\displaystyle G} an even number of times. These subgraphs are the elements of the cycle space of G {\displaystyle G} and are sometimes called cycles. If G {\displaystyle G} and H {\displaystyle H} are any two graphs, a function from the edges of G {\displaystyle G} to the edges of H {\displaystyle H} is defined to be cycle-continuous if the pre-image of every cycle of H {\displaystyle H} is a cycle of G {\displaystyle 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."