Bichromatic P4-composition schemes for perfect orderability Original Research Article

A P4 is an induced path with four vertices. A bichromatic P4 composition scheme is as follows: (1) start with two graphs with vertex sets of different colour, say black • and white ∘, (2) select a set of allowable four-vertex bichromatic sequences, for example {••••,∘∘∘∘,•∘∘•,∘••∘}, (3) add edges between the graphs so that in the composed graph each P4 is coloured with an allowable sequence. Answering a question of Chvátal, we determine all such schemes which preserve perfect orderability.