Forbidden Induced Pairs for Perfectness and $\omega$-Colourability of Graphs

We characterise the pairs of graphs $\{ X, Y \}$ such that all \}$-free (distinct from $C_5$) are perfect. Similarly, we $\omega$-colourable (that is, their chromatic number is equal to clique number). More generally, show characterizations for perfectness and $\omega$-colourability connected which independence at least~$3$, distinct an odd cycle, order least $n_0$, similar characterisations subject each subset these additional constraints. (The classes non-hereditary different.) build on recent results Brause et al. K_{1,3}, graphs, use Ramsey's Theorem Strong Perfect Graph as main tools. relate present known forbidden $\chi$-boundedness deciding $k$-colourability in polynomial time.