Journal article

Perfectness of clustered graphs


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  • 2013
Published in:
  • Discrete Optimization. - Elsevier BV. - 2013, vol. 10, no. 4, p. 296-303
English Given a clustered graph (G,P), that is, a graph G = (V, E) together with a partition P of its vertex set, the selective coloring problem consists in choosing one vertex per cluster such that the chromatic number of the subgraph induced by the chosen vertices is minimum. This problem can be formulated as a covering problem with a 0–1 matrix M(G,P). Nevertheless, we observe that, given (G,P), it is NP-hard to check if M(G,P) is conformal (resp. perfect).We will give a sufficient condition, checkable in polynomial time, for M(G,P) to be conformal that becomes also necessary if conformality is required to be hereditary. Finally, we show that M(G,P) is perfect for every partition P if and only if G belongs to a superclass of threshold graphs defined with a complex function instead of a real one.
Faculté des sciences économiques et sociales et du management
Département d'informatique
  • English
Computer science
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