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Seminaire MASCOTTEAcyclic edge coloring
par Nathann Cohen
A proper edge-colouring with the property that every cycle contains edges of at least three distinct colours is called an acyclic edge-colouring. The acyclic chromatic index of a graph $G$,
denoted $chi'_a(G)$ is the minimum $k$ such that $G$ admits an acyclic edge-colouring with $k$ colours.
We conjecture that if $G$ is planar and $Delta(G)$ is large enough then $chi'_a(G)=Delta(G)$. We settle this conjecture for planar graphs with girth at least $5$ and outerplanar graphs. We also show that $chi'_a(G)leq Delta(G) + 25$ for all planar $G$, which improves a previous result by Muthu et al.
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