A number of old conjectures related to edge-colourings of 3-regular graphs remain vastly open. Among them, the Petersen colouring conjecture is a very strong statement, which implies most of these, such as the Berge—Fulkerson conjecture, and the 5-Cycle-double-cover conjecture. It states that every bridgeless cubic graph admits an edge-colouring with 5 colours such that for every edge e, the set of colours assigned to the edges adjacent to e has cardinality either 2 or 4, but not 3.