Ekim, Tinaz, Ries, Bernard and de Werra, Dominique. (2010) Split-critical and uniquely split-colorable graphs. Discrete Mathematics & Theoretical Computer Science, Vol.12 (No.5). pp. 1-24. ISSN 1365-8050

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Abstract

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.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software Q Science > QA Mathematics
Divisions:	Faculty of Social Sciences > Warwick Business School
Journal or Publication Title:	Discrete Mathematics & Theoretical Computer Science
Publisher:	D M T C S
ISSN:	1365-8050
Date:	2010
Volume:	Vol.12
Number:	No.5
Number of Pages:	24
Page Range:	pp. 1-24
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Open Access
Funder:	B.U. Research Fund, Centre for Discrete Mathematics and Its Applications (DIMAP), University of Warwick, FNR
Grant number:	09A302P, TR-PDR BFR08-17
URI:	http://wrap.warwick.ac.uk/id/eprint/4752

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