Geodesic
Equitable Coloring and Equitable Choosability of Graphs with Small Maximum Average Degree
Discussiones Mathematicae. Graph Theory, Tome 38 (2018) no. 3, pp. 829-839

Voir la notice de l'article provenant de la source Library of Science

A graph is said to be equitably k-colorable if the vertex set V (G) can be partitioned into k independent subsets V_1, V_2, . . ., V_k such that | | V_i |−| V_j | | ≤ 1 (1 ≤ i, j ≤ k). 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 |V(G)|/ k vertices. In this paper, we prove that if G is a graph such that mad(G) lt; 3, then G is equitably k-colorable and equitably k- choosable where k ≥max{Δ (G), 4 }. Moreover, if G is a graph such that mad(G) lt; 12/5, then G is equitably k-colorable and equitably k-choosable where k ≥max{Δ (G), 3 }.
Keywords: graph coloring, equitable choosability, maximum average degree 
@article{DMGT_2018_38_3_a12,
     author = {Dong, Aijun and Zhang, Xin},
     title = {Equitable {Coloring} and {Equitable} {Choosability} of {Graphs} with {Small} {Maximum} {Average} {Degree}},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {829--839},
     publisher = {mathdoc},
     volume = {38},
     number = {3},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2018_38_3_a12/}
}
TY  - JOUR
AU  - Dong, Aijun
AU  - Zhang, Xin
TI  - Equitable Coloring and Equitable Choosability of Graphs with Small Maximum Average Degree
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2018
SP  - 829
EP  - 839
VL  - 38
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_2018_38_3_a12/
LA  - en
ID  - DMGT_2018_38_3_a12
ER  - 
%0 Journal Article
%A Dong, Aijun
%A Zhang, Xin
%T Equitable Coloring and Equitable Choosability of Graphs with Small Maximum Average Degree
%J Discussiones Mathematicae. Graph Theory
%D 2018
%P 829-839
%V 38
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2018_38_3_a12/
%G en
%F DMGT_2018_38_3_a12
Dong, Aijun; Zhang, Xin. Equitable Coloring and Equitable Choosability of Graphs with Small Maximum Average Degree. Discussiones Mathematicae. Graph Theory, Tome 38 (2018) no. 3, pp. 829-839. http://geodesic.mathdoc.fr/item/DMGT_2018_38_3_a12/