Editing Petersen graph (section)

== Petersen coloring conjecture ==
An ''Eulerian subgraph'' of a graph <math>G</math> is a subgraph consisting of a subset of the edges of <math>G</math>, touching every vertex of <math>G</math> an even number of times. These subgraphs are the elements of the [[cycle space]] of <math>G</math> and are sometimes called cycles. If <math>G</math> and <math>H</math> are any two graphs, a function from the edges of <math>G</math> to the edges of <math>H</math> is defined to be ''cycle-continuous'' if the pre-image of every cycle of <math>H</math> is a cycle of <math>G</math>. 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|cycle-double-cover]] conjecture and the Berge-Fulkerson conjecture."<ref>{{citation| last1 = DeVos | first1 = Matt
 | last2 = Nešetřil | first2 = Jaroslav | author2-link = Jaroslav Nešetřil
 | last3 = Raspaud | first3 = André
 | contribution = On edge-maps whose inverse preserves flows or tensions
 | doi = 10.1007/978-3-7643-7400-6_10
 | location = Basel
 | mr = 2279171
 | pages = 109–138
 | publisher = Birkhäuser
 | series = Trends Math.
 | title = Graph theory in Paris
 | year = 2007| isbn = 978-3-7643-7228-6
 }}.</ref>