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. Last, we give approximability and inapproximability results for general and restricted classes of graphs, and establish a FPT algorithm for interval graphs.
CITATION STYLE
Anglés D’Auriac, J. A., Bujtàs, C., El Maftouhi, H., Karpinski, M., Manoussakis, Y., Montero, L., … Tuza, Z. (2016). Tropical dominating sets in vertex-coloured graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9627, pp. 17–27). Springer Verlag. https://doi.org/10.1007/978-3-319-30139-6_2
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