Complexity of choosability with a small palette of colors
Abstract
A graph is $\ell$choosable if, for any choice of lists of $\ell$ colors for each vertex, there is a list coloring, which is a coloring where each vertex receives a color from its list. We study complexity issues of choosability of graphs when the number $k$ of colors is limited. We get results which differ surprisingly from the usual case where $k$ is implicit and which extend known results for the usual case. We also exhibit some classes of graphs (defined by structural properties of their blocks) which are choosable.
 Publication:

arXiv eprints
 Pub Date:
 January 2016
 arXiv:
 arXiv:1601.01768
 Bibcode:
 2016arXiv160101768D
 Keywords:

 Computer Science  Discrete Mathematics;
 Mathematics  Combinatorics
 EPrint:
 31 pages, 11 figures