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Independent sets of maximum weight in apple-free graphs

By Andreas Brandstädt, Vadim V. Lozin and Raffaele Mosca

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

Topics: QA
Publisher: Society for Industrial and Applied Mathematics
Year: 2010
OAI identifier: oai:wrap.warwick.ac.uk:3314

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