Geodesic
Defective choosability of graphs without small minors
The electronic journal of combinatorics, Tome 16 (2009) no. 1
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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.
DOI : 10.37236/181
Classification : 05C15
Mots-clés : list colouring, defective choosability, minor-free graph 
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     author = {Rupert G. Wood and Douglas R. Woodall},
     title = {Defective choosability of graphs without small minors},
     journal = {The electronic journal of combinatorics},
     year = {2009},
     volume = {16},
     number = {1},
     doi = {10.37236/181},
     zbl = {1186.05060},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/181/}
}
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Rupert G. Wood; Douglas R. Woodall. Defective choosability of graphs without small minors. The electronic journal of combinatorics, Tome 16 (2009) no. 1. doi: 10.37236/181

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