Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1141456 | Discrete Optimization | 2013 | 8 Pages |
Abstract
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.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Control and Optimization
Authors
Flavia Bonomo, Denis Cornaz, Tınaz Ekim, Bernard Ries,