k-forested choosability of graphs with bounded maximum average degree

Details k-forested choosability of graphs with bounded maximum average degree k-forested choosability of graphs with bounded maximum average degree

2011-02-19

arxiv.org/abs/1102.3987v1

Mathematics

Combinatorics

Please cite this paper in press as X. Zhang, G. Liu, J.-L. Wu, k-forested choosability of graphs with bounded maximum average

Scientific paper

A proper vertex coloring of a simple graph is $k$-forested if the graph induced by the vertices of any two color classes is a forest with maximum degree less than $k$. A graph is $k$-forested $q$-choosable if for a given list of $q$ colors associated with each vertex $v$, there exists a $k$-forested coloring of $G$ such that each vertex receives a color from its own list. In this paper, we prove that the $k$-forested choosability of a graph with maximum degree $\Delta\geq k\geq 4$ is at most $\lceil\frac{\Delta}{k-1}\rceil+1$, $\lceil\frac{\Delta}{k-1}\rceil+2$ or $\lceil\frac{\Delta}{k-1}\rceil+3$ if its maximum average degree is less than 12/5, $8/3 or 3, respectively.

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