Two-colourings that decompose perfect graphs

AbstractWe show that there are, up to a trivial equivalence, precisely six theorems of the following form: If the vertices of a graph G are coloured red and white in such a way that no chordless path with four vertices is coloured in certain ways (specified by the particular theorem), then G is perfect if and only if each of the two subgraphs of G induced by all the vertices of the same colour is perfect. One of these theorems was proved earlier by Chvátal and Hoàng; the remaining five are new