@article {
author = {Zhang, X. and Liu, G. and Wu, J.},
title = {k-forested choosability of graphs with bounded maximum average degree},
journal = {Bulletin of the Iranian Mathematical Society},
volume = {38},
number = {1},
pages = {193-201},
year = {2012},
publisher = {Iranian Mathematical Society (IMS)},
issn = {1017-060X},
eissn = {1735-8515},
doi = {},
abstract = {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 $\left\lceil\frac{\Delta}{k-1}\right\rceil+1$, $\left\lceil\frac{\Delta}{k-1}\right\rceil+2$ or $\left\lceil\frac{\Delta}{k-1}\right\rceil+3$ if its maximum average degree is less than $\frac{12}{5}$, $\frac{8}{3}$ or $3$, respectively.},
keywords = {k-forested coloring,linear coloring,maximum average degree},
url = {http://bims.iranjournals.ir/article_400.html},
eprint = {http://bims.iranjournals.ir/article_400_33c983c4321f08451943d77a341f126b.pdf}
}