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Generalizations of independence and chromatic numbers of a graph

✍ Scribed by E. Sampathkumar

Publisher: Elsevier Science
Year: 1993
Tongue: English
Weight: 426 KB
Volume: 115
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(93)90493-d

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✦ Synopsis

Sampathkumar, E., Generalizations of independence and chromatic numbers of a graph, Discrete Mathematics 115 (1993) 2455251. Let G = (V, E) be a graph and k > 2 be an integer. A set S c V is k-independent if every component in the subgraph (S) induced by S has order at most k-1. The general chromatic number xP(G) of G is the minimum order n of a partition P of the set V such that each set V, in P is k-independent, This paper develops properties of x~(C) which are generalizations of well-known properties of chromatic number.

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## Abstract We study a generalization of the notion of the chromatic number of a graph in which the colors assigned to adjacent vertices are required to be, in a certain sense, far apart. © 1993 John Wiley & Sons, Inc.