Editing Perfect graph (section)

==Related concepts==
Generalizing the perfect graphs, a graph class is said to be [[χ-bounded]] if the chromatic number of the graphs in the class can be bounded by a function of their clique number. The perfect graphs are exactly the graphs for which this function is the [[identity function|identity]], both for the graph itself and for all its induced subgraphs.{{r|gyarfas-1987}}

The equality of the clique number and chromatic number in perfect graphs has motivated the definition of other graph classes, in which other graph invariants are set equal to each other. For instance, the [[domination perfect graph]]s are defined as graphs in which, in every induced subgraph, the smallest dominating set (a set of vertices adjacent to all remaining vertices) equals the size of the smallest independent set that is a dominating set. These include, for instance, the [[claw-free graph]]s.{{r|ffr-1997}}