Recognition of graphs with convex quadratic stability number
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 i...
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| Formato: | conferenceObject |
| Idioma: | eng |
| Publicado em: |
2010
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| Texto completo: | http://hdl.handle.net/10198/1271 |
| País: | Portugal |
| Oai: | oai:bibliotecadigital.ipb.pt:10198/1271 |
| Resumo: | 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. |
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