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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
##### Keywords:
list colouring; defective choosability; minor-free graph
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