Tropical Dominating Sets in Vertex-Coloured Graphs
Discrete Mathematics
2016-01-19 v3
Abstract
Given a vertex-coloured graph, a dominating set is said to be tropical if every colour of the graph appears at least once in the set. Here, we study minimum tropical dominating sets from structural and algorithmic points of view. First, we prove that the tropical dominating set problem is NP-complete even when restricted to a simple path. Then, we establish upper bounds related to various parameters of the graph such as minimum degree and number of edges. We also give upper bounds for random graphs. Last, we give approximability and inapproximability results for general and restricted classes of graphs, and establish a FPT algorithm for interval graphs.
Cite
@article{arxiv.1503.01008,
title = {Tropical Dominating Sets in Vertex-Coloured Graphs},
author = {J. -A. Angles d'Auriac and Cs. Bujtas and A. El Maftouhi and M. Karpinski and Y. Manoussakis and L. Montero and N. Narayanan and L. Rosaz and J. Thapper and Zs. Tuza},
journal= {arXiv preprint arXiv:1503.01008},
year = {2016}
}
Comments
19 pages, 4 figures