A note on strong perfectness of graphs

In (strongly) perfect graphs, we define (strongly) canonical colorings; we show that for some classes of graphs, such colorings can be obtained by sequential coloring techniques. Chromatic properties ofP ₄-free graphs based on such coloring techniques are mentioned and extensions to graphs containing no inducedP ₅, orC ₅ are presented. In particular we characterize the class of graphs in which any maximal (or minimal) nodex in the vicinal preorder has the following property: there is either noP ₄ havingx as a midpoint or noP ₄ havingx as an endpoint. For such graphs, according to a result of Chvatal, there is a simple sequential coloring algorithm.