Stability number of bull- and chair-free graphs
Discrete Applied Mathematics
Polynomially solvable cases for the maximum stable set problem
Discrete Applied Mathematics - Special volume: Aridam VI and VII, Rutcor, New Brunswick, NJ, USA (1991 and 1992)
Polynomial algorithms for the maximum stable set problem on particular classes of P5-free graphs
Information Processing Letters
Bipartite graphs without a skew star
Discrete Mathematics
On easy and hard hereditary classes of graphs with respect to the independent set problem
Discrete Applied Mathematics - Special issue on stability in graphs and related topics
Discrete Applied Mathematics
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The augmenting chain technique has been applied to solve the maximum stable set problem in the class of line graphs (which coincides with the maximum matching problem) and then has been extended to the class of claw-free graphs. In the present paper, we propose a further generalization of this approach. Specifically, we show how to find an augmenting chain in graphs containing no skew star, i.e. a tree with exactly three vertices of degree 1 of distances 1, 2, 3 from the only vertex of degree 3. As a corollary, we prove that the maximum stable set problem is polynomially solvable in a class that strictly contains claw-free graphs, improving several existing results.