  The class of 2K2-free graphs and its various subclasses have been studied in
a variety of contexts. In this paper, we are concerned with the colouring of
(P3UP2)-free graphs, a super class of 2K2-free graphs. We derive a O(w^3) upper
bound for the chromatic number of (P3UP2)-free graphs, and sharper bounds for
(P3UP2), diamond)-free graphs, where w denotes the clique number. By applying
similar proof techniques we obtain chromatic bounds for (2K2, diamond)-free
graphs. The last two classes are perfect if w >=5 and >= 4 respectively.
