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 $k\geq\max\{\Delta(G), 7\}$.
@article{DMTCS_2019_21_3_a23,
author = {Dong, Aijun and Wu, Jianliang},
title = {Equitable {Coloring} and {Equitable} {Choosability} of {Planar} {Graphs} without chordal 4- and {6-Cycles}},
journal = {Discrete mathematics & theoretical computer science},
publisher = {mathdoc},
volume = {21},
number = {3},
year = {2019},
doi = {10.23638/DMTCS-21-3-16},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-21-3-16/}
}
TY - JOUR AU - Dong, Aijun AU - Wu, Jianliang TI - Equitable Coloring and Equitable Choosability of Planar Graphs without chordal 4- and 6-Cycles JO - Discrete mathematics & theoretical computer science PY - 2019 VL - 21 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-21-3-16/ DO - 10.23638/DMTCS-21-3-16 LA - en ID - DMTCS_2019_21_3_a23 ER -
%0 Journal Article %A Dong, Aijun %A Wu, Jianliang %T Equitable Coloring and Equitable Choosability of Planar Graphs without chordal 4- and 6-Cycles %J Discrete mathematics & theoretical computer science %D 2019 %V 21 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-21-3-16/ %R 10.23638/DMTCS-21-3-16 %G en %F DMTCS_2019_21_3_a23
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
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