Petersen graph

Petersen coloring conjecture ★★★

Author(s): Jaeger

Conjecture   Let $ G $ be a cubic graph with no bridge. Then there is a coloring of the edges of $ G $ using the edges of the Petersen graph so that any three mutually adjacent edges of $ G $ map to three mutually adjancent edges in the Petersen graph.

Keywords: cubic; edge-coloring; Petersen graph

4-flow conjecture ★★★

Author(s): Tutte

Conjecture   Every bridgeless graph with no Petersen minor has a nowhere-zero 4-flow.

Keywords: minor; nowhere-zero flow; Petersen graph

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