EEMCS EPrints Service

Education

Research

Prospective Students

Jobs

Publications

Intranet (internal)

Nederlands

Contact

Sitemap

Organisation

15830 Backbone colorings along stars and matchings in split graphs: their span is close to the chromatic number

Home Policy Brochure Browse Search User Area Contact Help

Broersma, H.J. and Marchal, L. and Paulusma, D. and Salman, A.N.M. (2009) Backbone colorings along stars and matchings in split graphs: their span is close to the chromatic number. Discussiones Mathematicae Graph Theory, 29 (1). pp. 143-162. ISSN 1234-3099

Full text available as:

HTML

- Univ. of Twente only
5 Kb

Official URL: http://www.discuss.wmie.uz.zgora.pl//gt/29_1/gt29-561.htm

Abstract

We continue the study on backbone colorings, a variation on classical vertex colorings that was introduced at WG2003. Given a graph $G = (V,E)$ and a spanning subgraph $H$ of $G$ (the backbone of $G$ ), a $\gamma$ -backbone coloring for $G$ and $H$ is a proper vertex coloring $V\to \{1,2,\ldots\}$ of $G$ in which the colors assigned to adjacent vertices in $H$ differ by at least $\gamma$ . The algorithmic and combinatorial properties of backbone colorings have been studied for various types of backbones in a number of papers. The main outcome of earlier studies is that the minimum number $\ell$ of colors, for which such colorings $V\to \{1,2,\ldots, \ell\}$ exist, in the worst case is a factor times the chromatic number (for path, tree, matching and star backbones). We show here that for split graphs and matching or star backbones, $\ell$ is at most a small additive constant (depending on $\gamma$ ) higher than the chromatic number. Our proofs combine algorithmic and combinatorial arguments. We also indicate other graph classes for which our results imply better upper bounds on $\ell$ than the previously known bounds.

Item Type:	Article
Research Group:	EWI-DMMP: Discrete Mathematics and Mathematical Programming
Research Program:	CTIT-IE&ICT: Industrial Engineering and ICT
ID Code:	15830
Status:	Published
Deposited On:	28 August 2009
Refereed:	Yes
International:	Yes
More Information:	statistics metis

Export this item as:

To request a copy of the PDF please email us request copy

To correct this item please ask your editor

Repository Staff Only: edit this item