Stability number of bull- and chair-free graphs revisited

De Simone showed that prime bull- and chair-free graphs containing a co-diamond are either bipartite or an induced cycle of odd length at least five. Based on this result, we give a complete structural characterization of prime (bull,chair)-free graphs having stability number at least four as well as of (bull,chair,co-chair)-free graphs. This implies constant-bounded clique width for these graph classes which leads to linear time algorithms for some algorithmic problems. Moreover, we obtain a robust O(nm) time algorithm for the maximum weight stable set problem on bull-and chair-free graphs without testing whether the (arbitrary) input graph is bull- and chair-free. This improves previous results with respect to structural insight, robustness and time bounds.

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