Perfectness of clustered graphs

• Autores: Bonomo, Flavia; Cornaz, Deni; Ekim, Tinaz; Ries, Bernard
• Año de publicación: 2013
• Idioma: inglés
• Tipo de recurso: artículo
• Fuente: CiteSeerX
• Materia: CONFORMAL MATRIX; PARTITION COLORING; PERFECT MATRIX; SELECTIVE COLORING; THRESHOLD GRAPH
• Institución: Consejo Nacional de Investigaciones Científicas y Técnicas

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.
Fil: Bonomo, Flavia. Consejo Nacional de Invest.cientif.y Tecnicas. Oficina de Coordinacion Administrativa Ciudad Universitaria. Instituto de Investigaciones Matematicas; Argentina
Fil: Cornaz, Deni. Université Paris-Dauphine; Francia
Fil: Ekim, Tinaz. Boğaziçi University; Turquía
Fil: Ries, Bernard. Université Paris-Dauphine; Francia