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.
@article{bwmeta1.element.doi-10_7151_dmgt_1786,
author = {Krzysztof Turowski},
title = {Optimal Backbone Coloring of Split Graphs with Matching Backbones},
journal = {Discussiones Mathematicae Graph Theory},
volume = {35},
year = {2015},
pages = {157-169},
zbl = {1307.05078},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1786}
}
Krzysztof Turowski. Optimal Backbone Coloring of Split Graphs with Matching Backbones. Discussiones Mathematicae Graph Theory, Tome 35 (2015) pp. 157-169. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1786/
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