Stability number of bull- and chair-free graphs

Efficient robust algorithms for the Maximum Weight Stable Set Problem in chair-free graph classes

“…Our algorithm, however, may compute α w (G) correctly also for some input graphs containing a chair; the smallest example is the chair itself. Moreover, we extend a result by De Simone and Sassano [13] on bull-and chair-free graphs.…”

“…Note also that already in [2] an O(n · m) time robust algorithm for MWS on (chair, bull)-free graphs is given improving the result of [13].…”

A polynomial algorithm to find an independent set of maximum weight in a fork-free graph

“…One of them deals with the subclass of fork-free graphs defined by forbidding additionally a graph known in the literature as a bull or an A-graph (the letter A being a graphical representation of the graph). A solution to the unweighted version of the problem in the class of (fork, bull)-free graphs has been proposed by De Simone in [15]. To solve the problem, she used a clique reduction, one of the two graph transformations employed by Lovász and Plummer in order to reduce the problem from claw-free to line graphs.…”

Augmenting chains in graphs without a skew star

“…Another way to reduce the maximum stable set problem from claw-free graphs to line graphs has been proposed by Lovász and Plummer in [7]. In 1999, Alekseev [1] extended the solution for claw-free graphs and some other polynomial-time results [4,6] to the class of chair-free graphs. He has shown that every connected chair-free augmenting graph is either a chain or an almost complete bipartite graph (i.e.…”