List-coloring graphs without K4,k-minors

Authors:
Ken-ichi Kawarabayashi
Affiliations:
The National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo 101-8430, Japan
Venue:
Discrete Applied Mathematics
Year:
2009

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Abstract

In this note, it is shown that every graph with no K"4","k-minor is 4k-list-colorable. We also give an extremal function for the existence for a K"4","k-minor. Our proof implies that there is a linear time algorithm for showing that either G has a K"4","k-minor or G is 4k-choosable. In fact, if the latter holds, then the algorithm gives rise to a 4k-list-coloring.