The problem
Every bridgeless cubic graph admits a normal edge-mapping into the Petersen graph (a Petersen colouring).
The Petersen colouring conjecture
openHistory & significance
Jaeger (1988) proposed the Petersen graph as a universal target for bridgeless cubic graphs — a common roof over the cycle double cover, Berge–Fulkerson, and five-flow conjectures, since a Petersen colouring implies all three. Partial results cover large girth and planar cases; the general statement is wide open, and its position as the strongest of the cubic-graph conjectures makes it the natural summit: prove Petersen colouring and three famous problems fall at once.
Connected problems
More in Graph theory
- same area The strong perfect graph theorem
- same area The total colouring conjecture
- same area The Goldberg–Seymour conjecture
References
Still open.
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