Stability number of bull- and chair-free graphs revisited

Andreas Brandstädt, Chı́nh T Hoàng, Van Bang Le
2003 Discrete Applied Mathematics  
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 ÿve. 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
more » ... st O(nm) time algorithm for the maximum weight stable set problem on bulland 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. ?
doi:10.1016/s0166-218x(02)00415-8 fatcat:vjokgbfafzbltiuxl66ercn5zu