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Article Dans Une Revue Journal of Combinatorial Theory, Series B Année : 2012

Combinatorial optimization with 2-joins.

Résumé

A 2-join is an edge cutset that naturally appears in decomposition of several classes of graphs closed under taking induced sub-graphs, such as perfect graphs and claw-free graphs. In this paper we construct combinatorial polynomial time algorithms for finding a maximum weighted clique, a maximum weighted stable set and an optimal coloring for a class of perfect graphs decomposable by 2-joins: the class of perfect graphs that do not have a balanced skew partition, a 2-join in the complement, nor a homogeneous pair. The techniques we develop are general enough to be easily applied to finding a maximum weighted stable set for another class of graphs known to be decomposable by 2-joins, namely the class of even-hole-free graphs that do not have a star cutset. We also give a simple class of graphs decomposable by 2-joins into bipartite graphs and line graphs, and for which finding a maximum stable set is NP-hard. This shows that having holes all of the same parity gives essential properties for the use of 2-joins in computing stable sets

Dates et versions

hal-00800197 , version 1 (13-03-2013)

Identifiants

Citer

Nicolas Trotignon, Vuskovic Kristina. Combinatorial optimization with 2-joins.. Journal of Combinatorial Theory, Series B, 2012, 102, pp.153-185. ⟨10.1016/j.jctb.2011.06.002⟩. ⟨hal-00800197⟩
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