 |
Discrete Mathematics & Theoretical Computer Science |
Min Chen ; André Raspaud ; Weifan Wang - 8-star-choosability of a graph with maximum average degree less than 3
dmtcs:561 - Discrete Mathematics & Theoretical Computer Science, December 31, 2011, Vol. 13 no. 3 - https://doi.org/10.46298/dmtcs.561- 1 Department of Mathematics [Jinhua]
- 2 Laboratoire Bordelais de Recherche en Informatique
A proper vertex coloring of a graphGis called a star-coloring if there is no path on four vertices assigned to two colors. The graph G is L-star-colorable if for a given list assignment L there is a star-coloring c such that c(v) epsilon L(v). If G is L-star-colorable for any list assignment L with vertical bar L(v)vertical bar \textgreater= k for all v epsilon V(G), then G is called k-star-choosable. The star list chromatic number of G, denoted by X-s(l)(G), is the smallest integer k such that G is k-star-choosable. In this article, we prove that every graph G with maximum average degree less than 3 is 8-star-choosable. This extends a result that planar graphs of girth at least 6 are 8-star-choosable [A. Kundgen, C. Timmons, Star coloring planar graphs from small lists, J. Graph Theory, 63(4): 324-337, 2010].
