Well-hued graphs.

We define a graph G as well-hued if for each positive integer k there is an integer a k such that every maximal k -colorable subgraph of G has order a k. This strengthens the notion of well-covered graphs. In this paper we investigate the connection between this property and related properties, characterize the sequences of the a k that can be achieved, and determine conditions for the property in some graph classes and under some graph operations such as products. [ABSTRACT FROM AUTHOR]