Abstract
The Minimum Dominating Set problem remains NP-hard when restricted to chordal graphs, circle graphs and c-dense graphs (i.e. |E| ≥cn 2 for a constant c, 0<c<1/2). For each of these three graph classes we present an exponential time algorithm solving the Minimum Dominating Set problem. The running times of those algorithms are O(1.4173n) for chordal graphs, O(1.4956n) for circle graphs, and \(O(1.2303^{(1+\sqrt{1-2c})n})\) for c-dense graphs.
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Gaspers, S., Kratsch, D., Liedloff, M. (2006). Exponential Time Algorithms for the Minimum Dominating Set Problem on Some Graph Classes. In: Arge, L., Freivalds, R. (eds) Algorithm Theory – SWAT 2006. SWAT 2006. Lecture Notes in Computer Science, vol 4059. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11785293_16
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DOI: https://doi.org/10.1007/11785293_16
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