On some applications of the selective graph coloring problem
European Journal of Operational Research, cilt.240, sa.2, ss.307-314, 2015 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Derleme
- Cilt numarası: 240 Sayı: 2
- Basım Tarihi: 2015
- Doi Numarası: 10.1016/j.ejor.2014.05.011
- Dergi Adı: European Journal of Operational Research
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.307-314
- Anahtar Kelimeler: Combinatorial optimization, Computational complexity, Graph theory, Partition coloring, Selective coloring
- Boğaziçi Üniversitesi Adresli: Evet
Özet
In this paper we present the Selective Graph Coloring Problem, a generalization of the standard graph coloring problem as well as several of its possible applications. Given a graph with a partition of its vertex set into several clusters, we want to select one vertex per cluster such that the chromatic number of the subgraph induced by the selected vertices is minimum. This problem appeared in the literature under different names for specific models and its complexity has recently been studied for different classes of graphs. Here, we describe different models - some already discussed in previous papers and some new ones - in very different contexts under a unified framework based on this graph problem. We point out similarities between these models, offering a new approach to solve them, and show some generic situations where the selective graph coloring problem may be used. We focus on specific graph classes motivated by each model, and we briefly discuss the complexity of the selective graph coloring problem in each one of these graph classes and point out interesting future research directions.