On claw-free asteroidal triple-free graphs

Harald Hempel, Dieter Kratsch
2002 Discrete Applied Mathematics  
We present an O(n 2:376 ) algorithm for recognizing claw-free AT-free graphs and a linear-time algorithm for computing the set of all central vertices of a claw-free AT-free graph. In addition, we give e cient algorithms that solve the problems INDEPENDENT SET, DOMINATING SET, and COLORING. We argue that all running times achieved are optimal unless better algorithms for a number of famous graph problems such as triangle recognition and bipartite matching have been found. Our algorithms exploit
more » ... the structure of 2LexBFS schemes of claw-free AT-free graphs. ?
doi:10.1016/s0166-218x(01)00208-6 fatcat:7isrygxg3ndvnpa6t5ud22bx6u