Recognition of graphs with convex quadratic stability number

Pacheco, Maria F.; Cardoso, Domingos M.

http://hdl.handle.net/10198/1271

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Authors

Pacheco, Maria F.

Cardoso, Domingos M.

Abstract(s)

A stable set of a graph is a set of mutually non-adjacent vertices. The determination of a maximum size stable set, which is called maximum stable set, and the determination of its size, which is called stability number, are central combinatorial optimization problems. However, given a nonnegative integer k, to determine if a graph G has a stable set of size k is NP-complete. In this paper we deal with graphs for which the stability number can be determined by solving a convex quadratic programming problem. Such graphs were introduced in [13] and are called graphs with convex-QP stability number. A few algorithmic techniques for the recognition of this type of graphs in particular families are presented.

Keywords

Graph theory Convex optimization

URI

http://hdl.handle.net/10198/1271

Citation

Pacheco, Maria F.; Cardoso, Domingos M. (2009). Recognition of graphs with convex quadratic stability number. In AIP Conference Proceedings - International Conference on Numerical Analysis and Applied Mathematics. p.1366-1369. ISBN 978-0-7354-0709.