Abstract
Let G=( V,E) be a graph and k⩾2 be an integer. A set S⊂ V is k-independent if every component in the subgraph < S⊂ induced by S has order at most k—1. The general chromatic number χ k ( G) of G is the minimum order n of a partition P of the set V such that each set V i in P is k-independent. This paper develops properties of χ k ( G) which are generalizations of well-known properties of chromatic number.
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