Scholarly article on topic 'Optimal backbone coloring of split graphs with matching backbones'

Optimal backbone coloring of split graphs with matching backbones Academic research paper on "Mathematics"

Share paper
Academic journal
Discuss. Math. Graph Theory
OECD Field of science

Academic research paper on topic "Optimal backbone coloring of split graphs with matching backbones"

Discussiones Mathematicae Graph Theory 35 (2015) 157-169 doi: 10.7151/dmgt. 1786



Gdansk University of Technology Department of Algorithms and System Modelling



For a graph G with a given subgraph H, the backbone coloring is defined as the mapping c : V(G) ^ N+ such that |c(u) — c(v)| > 2 for each edge {u,v} e E(H) and |c(u) — c(v)| > 1 for each edge {u,v} e E(G). The backbone chromatic number BBC(G, H) is the smallest integer k such that there exists a backbone coloring with max„£V(G) c(v) = k.

In this paper, we present the algorithm for the backbone coloring of split graphs with matching backbone.

Keywords: backbone coloring, split graphs, matching. 2010 Mathematics Subject Classification: 05C15.


[1] P. Hammer and S. Foldes, Split graphs, Congr. Numer. XIX (1977) 311-315.

[2] J. Miskuf, R. Skrekovski and M. Tancer, Backbone colorings of graphs with bounded degree, Discrete Appl. Math. 158 (2010) 534-542. doi:10.1016/j.dam.2009.11.015

[3] H. Broersma, F.V. Fomin, P.A. Golovach and G.J. Woeginger, Backbone colorings for graphs: tree and path backbones, J. Graph Theory 55 (2007) 137-152. doi:10.1002/jgt.20228

[4] H. Broersma, A general framework for coloring problems: old results, new results, and open problems, in: Combinatorial Geometry and Graph Theory: Indonesia-Japan Joint Conference, IJCCGGT 2003, Bandung, Indonesia, J. Akiyama, E.T. Baskoro, M. Kano (Ed(s)), (Springer, 2003) 65-79.

1This project has been partially supported by Narodowe Centrum Nauki under contract DEC-2011/02/A/ST6/00201.

[5] R. Janczewski, On an interrelation between travelling salesman problem and T-coloring of graphs, Proceedings of the Sixth International Conference: Advanced Computer Systems, ACS 1999, Szczecin, Poland (1999) 23-25.

Received 1 December 2011 Revised 18 November 2013 Accepted 1 May 2014

Copyright of Discussiones Mathematicae: Graph Theory is the property of Discussiones Mathematicae Graph Theory and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use.