Affiliation:
1. Department of Mathematics, Zhejiang Normal University, Zhejiang Jinhua, 321004, China
Abstract
The equitable chromatic number χe(G) of a graph G is the smallest integer k for which G has a proper k-coloring such that the number of vertices in any two color classes differ by at most one. In 1973, Meyer conjectured that the equitable chromatic number of a connected graph G, which is neither a complete graph nor an odd cycle, is at most Δ(G). We prove that this conjecture holds for 2-degenerate graphs with Δ(G) ≥ 5 and plane graphs without 3, 4 and 5 cycles.
Publisher
World Scientific Pub Co Pte Lt
Subject
Discrete Mathematics and Combinatorics
Reference11 articles.
1. A. Hajnal and E. Szeméredi, Combinatorial Theory and its Applications II, eds. P. Erdös, A. Rényi and V. T. Sós (North-Holland, Amsterdam, 1970) pp. 601–603.
2. Equitable Coloring
3. On equitable coloring of bipartite graphs
4. Equitable Coloring and the Maximum Degree
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