---
tag: 6KTFRQ251A
kind: statement
role: proposition
name: Petersen coloring conjecture
msc: [05C99]
sources:
  - wikipedia: en:194926@r1368629563
    locator: Petersen graph, section Petersen coloring conjecture
    note: adopted
    mention: wikipedia://en/194926#NDB9
    sections: [Statement]
inventory: [38KWF8R6WS]
---

## 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."