A fast algorithm for equitable coloring

Authors:
Henry A. Kierstead;Alexandr V. Kostochka;Marcelo Mydlarz;Endre Szemerédi
Affiliations:
Arizona State University, School of Mathematical and Statistical Sciences, P.O. Box 871804, 85287, Tempe, AZ, USA;University of Illinois, Department of Mathematics, 1409 W. Green St., 61801, Urbana, IL, USA and Sobolev Institute of Mathematics, Novosibirsk, 630090, Russia;Yahoo! Research Latin America, Blanco Encalada 2120, 4h floor, Santiago, Chile;Rutgers University, Department of Computer Science, 110 Frelinghuysen Rd., 08854-8019, Piscataway, NJ, USA
Venue:
Combinatorica
Year:
2010

Citing 0
Cited 4

A note on relaxed equitable coloring of graphs

Information Processing Letters
Approximate multipartite version of the Hajnal-Szemerédi theorem

Journal of Combinatorial Theory Series B
An improved upper bound on the density of universal random graphs

LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
Every 4-Colorable Graph With Maximum Degree 4 Has an Equitable 4-Coloring

Journal of Graph Theory

Quantified Score

Hi-index	0.00

Visualization

Abstract

A proper vertex coloring of a graph is equitable if the sizes of color classes differ by at most one. The celebrated Hajnal-Szemerédi Theorem states: For every positive integer r, every graph with maximum degree at most r has an equitable coloring with r+1 colors. We show that this coloring can be obtained in O(rn 2) time, where n is the number of vertices.