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Edge choosability of planar graphs without short cycles. (English) Zbl 1124.05037

The author proves that if \(G\) is a planar graph with maximum vertex degree \(\Delta= 5\) and without \(4\)- or \(6\)-cycles, then \(G\) is edge-\(6\)-choosable. It follows that for each \(k\in \{3,4,5,6\}\), a \(k\)-cycle-free planar graph \(G\) is edge-\((\Delta+ 1)\)-choosable.

MSC:

05C15 Coloring of graphs and hypergraphs
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