Finding augmenting chains in extensions of claw-free graphs

Authors:
A. Hertz;V. Lozin;D. Schindl
Affiliations:
GERAD-École Polytechnique, 3000 chemin de la Cote Sainte-Catherine, Montréal, QC, Canada H3T 2A7;RUTCOR, Rutgers University, Bartholomew Rd., Piscataway, NJ;Institute of Mathematics, Swiss Federal Institute of Technology, CH-1015 Lausanne, Switzerland
Venue:
Information Processing Letters
Year:
2003

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Abstract

Finding augmenting chains is in the heart of the maximum matching problem, which is equivalent to the maximum stable set problem in the class of line graphs. Due to the celebrated result of Edmonds, augmenting chains can be found in line graphs in polynomial time. Minty and Sbihi generalized this result to claw-free graphs. In this paper we extend it to larger classes. As a particular consequence, a new polynomially solvable case for the maximum stable set problem has been detected.