




Volume 35 • Number 4 • 2012 

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Equitable Coloring and Equitable Choosability of Planar Graphs Without 5 and 7Cycles
Aijun Dong, Xin Zhang and Guojun Li
Abstract.
A graph $G$ is equitably $k$choosable if for any $k$uniform list assignment $L$, $G$ is $L$colorable and each color appears on at most $\lceilV(G)/k\rceil$ vertices. A graph $G$ is equitable $k$colorable if $G$ has a proper vertex coloring with $k$ colors such that the size of the color classes differ by at most 1. In this paper, we prove that if $G$ is a planar graph without $5$ and $7$cycles, then $G$ is equitably $k$choosable and equitably $k$colorable where $k\geq\max\{\Delta(G),7\}$.
2010 Mathematics Subject Classification: 05C15.
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