The Seventh European Conference on Combinatorics, Graph Theory and Applications pp 241-244 | Cite as

# Planar graphs with Δ ≥ 8 are (Δ + 1)-edge-choosable

## Abstract

We consider the problem of *list edge coloring* for planar graphs. Edge coloring is the problem of coloring the edges while ensuring that two edges that are incident receive different colors. A graph is *k*-edge-choosable if for any assignment of *k* colors to every edge, there is an edge coloring such that the color of every edge belongs to its color assignment. Vizing conjectured in 1965 that every graph is (Δ + 1)-edge-choosable. In 1990, Borodin solved the conjecture for planar graphs with maximum degree Δ ≥ 9, and asked whether the bound could be lowered to 8. We prove here that planar graphs with Δ ≥ 8 are (Δ + 1)-edge-choosable.

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