Partitioning a graph into disjoint cliques and a triangle-free graph
A graph G=(V,E) is partitionable if there exists a partition {A,B} of V such that A induces a disjoint union of cliques (i.e. , G[A] is P3-free) and B induces a triangle-free graph (i.e. , G[B] is K3-free). In this paper we investigate the computational complexity of deciding whether a graph is part...
محفوظ في:
| المؤلف الرئيسي: | |
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| مؤلفون آخرون: | , |
| التنسيق: | article |
| منشور في: |
2015
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| الوصول للمادة أونلاين: | http://hdl.handle.net/10725/2779 http://dx.doi.org/10.1016/j.dam.2015.03.0151 http://www.sciencedirect.com/science/article/pii/S0166218X1500164X |
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| الملخص: | A graph G=(V,E) is partitionable if there exists a partition {A,B} of V such that A induces a disjoint union of cliques (i.e. , G[A] is P3-free) and B induces a triangle-free graph (i.e. , G[B] is K3-free). In this paper we investigate the computational complexity of deciding whether a graph is partitionable. The problem is known to be NP-complete on arbitrary graphs. Here it is proved that if a graph G is bull-free, planar, perfect, K4-free or does not contain certain holes then deciding whether G is partitionable is NP-complete. This answers an open question posed by Thomassé, Trotignon and Vušković. In contrast a finite list of forbidden induced subgraphs is given for partitionable cographs. |
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