Journal of Combinatorial Theory Series B
Equitable coloring and the maximum degree
European Journal of Combinatorics
On equitable coloring of bipartite graphs
Discrete Mathematics - Special issue on graph theory and combinatorics
Choosability and Edge Choosability of Planar Graphs without Intersecting Triangles
SIAM Journal on Discrete Mathematics
Equitable Colourings of d-degenerate Graphs
Combinatorics, Probability and Computing
A list analogue of equitable coloring
Journal of Graph Theory
Equitable list-coloring for graphs of maximum degree 3
Journal of Graph Theory
On the small cycle transversal of planar graphs
WG'10 Proceedings of the 36th international conference on Graph-theoretic concepts in computer science
On the small cycle transversal of planar graphs
Theoretical Computer Science
Equitable colorings of planar graphs without short cycles
Theoretical Computer Science
| Hi-index | 5.23 |
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 @?|V(G)|k@? vertices. A graph G is equitably k-colorable if G has a proper k-vertex coloring such that the sizes of any two color classes differ by at most 1. In this paper, we prove that every planar graph G is equitably k-choosable and equitably k-colorable if one of the following conditions holds: (1) G is triangle-free and k=max{@D(G),8}; (2) G has no 4- and 5-cycles and k=max{@D(G),7}.