Geodesic
Optimal Backbone Coloring of Split Graphs with Matching Backbones
Discussiones Mathematicae. Graph Theory, Tome 35 (2015) no. 1, pp. 157-169.

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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 max_v∈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 
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Turowski, Krzysztof. Optimal Backbone Coloring of Split Graphs with Matching Backbones. Discussiones Mathematicae. Graph Theory, Tome 35 (2015) no. 1, pp. 157-169. http://geodesic.mathdoc.fr/item/DMGT_2015_35_1_a12/

[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

[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.

[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.