Abstract.
Let P be a hereditary family of graphs. A relaxed coloring of a graph with respect to P is an assignment of colors to vertices of G so that each color class induces a graph which is the disjoint union of members of P. The P-chromatic number of G is the minimum number of colors in a relaxed coloring of G with respect to P. We study the relation between the girth and the P-chromatic number of a graph, and the P-chromatic number of product graphs. Our results generalize some results of M.L. Weaver and D.B. West in [10], and answer some questions in that paper.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received: January 9, 1995 / Revised: June 2, 1995
Rights and permissions
About this article
Cite this article
Deuber, W., Zhu, X. Relaxed Coloring of a Graph. Graphs Comb 14, 121–130 (1998). https://doi.org/10.1007/s003730050020
Issue Date:
DOI: https://doi.org/10.1007/s003730050020