Abstract
A graph $G$ is equitably $k$-choosable if, for any $k$-uniform list assignment $L$, $G$ admits a proper coloring $\pi$ such that $\pi(v)\in L(v)$ for all $v\in V(G)$ and each color appears on at most $\lceil |G|/k\rceil$ vertices. It was conjectured in [8] that every graph $G$ with maximum degree $\Delta$ is equitably $k$-choosable whenever $k\ge \Delta+1$. We prove the conjecture for the following cases: (i) $\Delta \le 3$; (ii) $k\ge (\Delta-1)^2$. Moreover, equitably 2-choosable graphs are completely characterized.
Citation
Wei-Fan Wang. Ko-Wei Lih. "EQUITABLE LIST COLORING OF GRAPHS." Taiwanese J. Math. 8 (4) 747 - 759, 2004. https://doi.org/10.11650/twjm/1500407716
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