Geodesic
Equitable Coloring and Equitable Choosability of Planar Graphs without chordal 4- and 6-Cycles
Discrete mathematics & theoretical computer science, Tome 21 (2019) no. 3.

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A graph $G$ is equitably $k$-choosable if, for any given $k$-uniform list assignment $L$, $G$ is $L$-colorable and each color appears on at most $\lceil\frac{|V(G)|}{k}\rceil$ vertices. A graph is equitably $k$-colorable if the vertex set $V(G)$ can be partitioned into $k$ independent subsets $V_1$, $V_2$, $\cdots$, $V_k$ such that $||V_i|-|V_j||\leq 1$ for $1\leq i, j\leq k$. In this paper, we prove that if $G$ is a planar graph without chordal $4$- and $6$-cycles, then $G$ is equitably $k$-colorable and equitably $k$-choosable where $k\geq\max\{\Delta(G), 7\}$.
DOI : 10.23638/DMTCS-21-3-16
Classification : 05C10, 05C15, 05C38, 05C70 
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     title = {Equitable {Coloring} and {Equitable} {Choosability} of {Planar} {Graphs} without chordal 4- and {6-Cycles}},
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Dong, Aijun; Wu, Jianliang. Equitable Coloring and Equitable Choosability of Planar Graphs without chordal 4- and 6-Cycles. Discrete mathematics & theoretical computer science, Tome 21 (2019) no. 3. doi : 10.23638/DMTCS-21-3-16. http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-21-3-16/

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