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• # Artykuł - szczegóły

## Discussiones Mathematicae Graph Theory

2015 | 35 | 1 | 157-169

## Optimal Backbone Coloring of Split Graphs with Matching Backbones

EN

### Abstrakty

EN
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(H) and |c(u) − c(v)| ≥ 1 for each edge {u, v} ∈ E(G). The backbone chromatic number BBC(G,H) is the smallest integer k such that there exists a backbone coloring with maxv∈V (G) c(v) = k. In this paper, we present the algorithm for the backbone coloring of split graphs with matching backbone.

EN

157-169

wydano
2015-02-01
otrzymano
2011-12-01
poprawiono
2013-11-18
zaakceptowano
2014-05-01
online
2015-02-06

### Twórcy

autor
• Gdańsk University of Technology Department of Algorithms and System Modelling

### Bibliografia

• [1] P. Hammer and S. Földes, Split graphs, Congr. Numer. XIX (1977) 311-315.
• [2] J. Miškuf, 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[Crossref][WoS]
• [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[Crossref][WoS]
• [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.
• [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.