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Defective choosability of graphs without small minors. (English) Zbl 1186.05060
Summary: For each proper subgraph \(H\) of \(K_5\), we determine all pairs \((k,d)\) such that every \(H\)-minor-free graph is \((k,d)^*\)-choosable or \((k, d)^-\)-choosable. The main structural lemma is that the only 3-connected \((K_5-e)\)-minor-free graphs are wheels, the triangular prism, and \(K_{3,3}\); this is used to prove that every \((K_5-e)\)-minor-free graph is 4-choosable and \((3,1)\)-choosable.

MSC:
05C15 Coloring of graphs and hypergraphs
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