Geodesic
Equitable Coloring and Equitable Choosability of Planar Graphs Without 5- and 7-Cycles
Bulletin of the Malaysian Mathematical Society, Tome 35 (2012) no. 4 Cet article a éte moissonné depuis la source Bulletin of the Malaysian Mathematical Society website

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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 $\lceil|V(G)|/k\rceil$ 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 $k\geq\max\{\Delta(G),7\}$.
Classification : 05C15. 
@article{BMMS_2012_35_4_a6,
     author = {Aijun Dong and Xin Zhang and Guojun Li},
     title = {Equitable {Coloring} and {Equitable} {Choosability} of {Planar} {Graphs} {Without} 5- and {7-Cycles}},
     journal = {Bulletin of the Malaysian Mathematical Society},
     year = {2012},
     volume = {35},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/BMMS_2012_35_4_a6/}
}
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Aijun Dong; Xin Zhang; Guojun Li. Equitable Coloring and Equitable Choosability of Planar Graphs Without 5- and 7-Cycles. Bulletin of the Malaysian Mathematical Society, Tome 35 (2012) no. 4. http://geodesic.mathdoc.fr/item/BMMS_2012_35_4_a6/