Planar graphs with Δ ≥ 8 are (Δ + 1)-edge-choosable
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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- K. Appel and W. Haken, Every map is four colorable: Part 1, Discharging, Illinois J. Math. 21 (1977), 422–490.Google Scholar
- M. Bonamy, Planar graphs with maximum degree D at least 8 are (D+1)-edge-choosable, preprint, http://arxiv.org/abs/1303.4025
- T. Jensen and B. Toft, “Graph Coloring Problems”, Wiley Interscience, New York (1995).Google Scholar