# Optimal Backbone Coloring of Split Graphs with Matching Backbones

• Volume: 35, Issue: 1, page 157-169
• ISSN: 2083-5892

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## Abstract

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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 maxv∈V (G) c(v) = k. In this paper, we present the algorithm for the backbone coloring of split graphs with matching backbone.

## How to cite

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Krzysztof Turowski. "Optimal Backbone Coloring of Split Graphs with Matching Backbones." Discussiones Mathematicae Graph Theory 35.1 (2015): 157-169. <http://eudml.org/doc/271216>.

@article{KrzysztofTurowski2015,
abstract = {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.},
author = {Krzysztof Turowski},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {backbone coloring; split graphs; matching},
language = {eng},
number = {1},
pages = {157-169},
title = {Optimal Backbone Coloring of Split Graphs with Matching Backbones},
url = {http://eudml.org/doc/271216},
volume = {35},
year = {2015},
}

TY - JOUR
AU - Krzysztof Turowski
TI - Optimal Backbone Coloring of Split Graphs with Matching Backbones
JO - Discussiones Mathematicae Graph Theory
PY - 2015
VL - 35
IS - 1
SP - 157
EP - 169
AB - 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.
LA - eng
KW - backbone coloring; split graphs; matching
UR - http://eudml.org/doc/271216
ER -

## References

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1. [1] P. Hammer and S. Földes, Split graphs, Congr. Numer. XIX (1977) 311-315.
2. [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] Zbl1215.05071
3. [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] Zbl1118.05031
4. [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. [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.

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