# Petersen graph

## Petersen coloring conjecture ★★★

Author(s): Jaeger

\begin{conjecture} Let $G$ be a \Def[cubic]{cubic graph} graph with no \Def[bridge]{bridge (graph theory)}. Then there is a coloring of the edges of $G$ using the edges of the \Def[Petersen]{petersen graph} graph so that any three mutually adjacent edges of $G$ map to three mutually adjancent edges in the Petersen graph. \end{conjecture}

Keywords: cubic; edge-coloring; Petersen graph

## 4-flow conjecture ★★★

Author(s): Tutte

\begin{conjecture} Every \Def[bridgeless]{bridge (graph theory)} graph with no \Def[Petersen]{petersen graph} \Def[minor]{minor (graph theory)} has a \Def[nowhere-zero]{nowhere-zero flows} 4-flow. \end{conjecture}

Keywords: minor; nowhere-zero flow; Petersen graph