Independent Sets of Maximum Weight in Apple-Free Graphs

Authors:
Andreas Brandstädt;Vadim V. Lozin;Raffaele Mosca
Affiliations:
ab@informatik.uni-rostock.de;V.Lozin@warwick.ac.uk;r.mosca@unich.it
Venue:
SIAM Journal on Discrete Mathematics
Year:
2010

Citing 14
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Abstract

We present the first polynomial-time algorithm to solve the maximum weight independent set problem for apple-free graphs, which is a common generalization of several important classes where the problem can be solved efficiently, such as claw-free graphs, chordal graphs, and cographs. Our solution is based on a combination of two algorithmic techniques (modular decomposition and decomposition by clique separators) and a deep combinatorial analysis of the structure of apple-free graphs. Our algorithm is robust in the sense that it does not require the input graph $G$ to be apple-free; the algorithm either finds an independent set of maximum weight in $G$ or reports that $G$ is not apple-free.