We use cookies to ensure that we give you the best experience on our website. By continuing to browse this repository, you give consent for essential cookies to be used. You can read more about our Privacy and Cookie Policy.

Durham Research Online
You are in:

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

Broersma, H. J. and Marchal, L. and Paulusma, Daniel 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.


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 l-backbone coloring for G and H is a proper vertex coloring V® {1,2,Ľ} of G in which the colors assigned to adjacent vertices in H differ by at least l. 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 l of colors, for which such colorings V® {1,2,Ľ,l} 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, l is at most a small additive constant (depending on l) 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 l than the previously known bounds.

Item Type:Article
Keywords:Backbone coloring, Split graph, Matching, Star
Full text:(VoR) Version of Record
Download PDF
Publisher Web site:
Record Created:09 Sep 2009 10:20
Last Modified:02 Apr 2013 16:52

Social bookmarking: del.icio.usConnoteaBibSonomyCiteULikeFacebookTwitterExport: EndNote, Zotero | BibTex
Look up in GoogleScholar | Find in a UK Library