Abstract
We prove that line graphs and path graphs have bounded neighbourhood Helly. As a consequence, we obtain output-polynomial time algorithms for enumerating the set of minimal dominating sets of line graphs and path graphs. Therefore, there exists an output-polynomial time algorithm that enumerates the set of minimal edge-dominating sets of any graph.
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Kanté, M.M., Limouzy, V., Mary, A., Nourine, L. (2012). On the Neighbourhood Helly of Some Graph Classes and Applications to the Enumeration of Minimal Dominating Sets. In: Chao, KM., Hsu, Ts., Lee, DT. (eds) Algorithms and Computation. ISAAC 2012. Lecture Notes in Computer Science, vol 7676. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35261-4_32
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DOI: https://doi.org/10.1007/978-3-642-35261-4_32
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