Split-critical and uniquely split-colorable graphs

Ekim, Tinaz; Ries, Bernard; de Werra, Dominique

Ekim, Tinaz; Ries, Bernard; de Werra, Dominique (2010), Split-critical and uniquely split-colorable graphs, Discrete Mathematics and Theoretical Computer Science, 12, 5, p. 1-24

Type

Article accepté pour publication ou publié

External document link

http://www.dmtcs.org/dmtcs-ojs/index.php/dmtcs/article/view/1479/3367

Date

2010

Journal name

Discrete Mathematics and Theoretical Computer Science

Volume

Number

Publisher

dmtcs

Pages

1-24

Metadata

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Author(s)

Ekim, Tinaz
Ries, Bernard
de Werra, Dominique

Abstract (EN)

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.

Subjects / Keywords

Split-coloring; split-critical; uniquely split-colorable; split-decreasing