Split-critical and uniquely split-colorable graphs
Discrete Mathematics and Theoretical Computer Science, cilt.12, sa.5, ss.1-24, 2010 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 12 Sayı: 5
- Basım Tarihi: 2010
- Dergi Adı: Discrete Mathematics and Theoretical Computer Science
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.1-24
- Anahtar Kelimeler: Split-coloring, Split-critical, Split-decreasing, Uniquely split-colorable
- Boğaziçi Üniversitesi Adresli: Evet
Özet
The split-coloring problem is a generalized vertex coloring problem where we partition the vertices into a minimum number of split graphs. In this paper, we study some notions which are extensively studied for the usual vertex coloring and the cocoloring problem from the point of view of split-coloring, such as criticality and the uniqueness of the minimum split-coloring. We discuss some properties of split-critical and uniquely split-colorable graphs. We describe constructions of such graphs with some additional properties. We also study the effect of the addition and the removal of some edge sets on the value of the split-chromatic number. All these results are compared with their cochromatic counterparts. We conclude with several research directions on the topic. © 2010 Discrete Mathematics and Theoretical Computer Science.