Perfectness of clustered graphs
Discrete Optimization, cilt.10, sa.4, ss.296-303, 2013 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 10 Sayı: 4
- Basım Tarihi: 2013
- Doi Numarası: 10.1016/j.disopt.2013.07.006
- Dergi Adı: Discrete Optimization
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.296-303
- Anahtar Kelimeler: Conformal matrix, Partition coloring, Perfect matrix, Selective coloring, Threshold graph
- Boğaziçi Üniversitesi Adresli: Evet
Özet
Given a clustered graph (G,V), that is, a graph G=(V,E) together with a partition V 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,V). Nevertheless, we observe that, given (G,V), it is NP-hard to check if M(G,V) is conformal (resp. perfect). We will give a sufficient condition, checkable in polynomial time, for M(G,V) to be conformal that becomes also necessary if conformality is required to be hereditary. Finally, we show that M(G,V) is perfect for every partition V if and only if G belongs to a superclass of threshold graphs defined with a complex function instead of a real one.