k-forested choosability of graphs with bounded maximum average degree
英文摘要：
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 $Δ\geq k\geq 4$ is at most $\lceil\fracΔ{k-1}\rceil+1$, $\lceil\fracΔ{k-1}\rceil+2$ or $\lceil\fracΔ{k-1}\rceil+3$ if its maximum average degree is less than 12/5, $8/3 or 3, respectively.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
