Abstract
A connected dominating set (CDS) of a graph, G, is a set of vertices, C ⊆ V(G), such that every vertex in V(G) ∖ C is incident to at least one vertex of C in G and the subgraph induced by the vertices of C in G is connected. In this paper we consider a simple, yet efficient, randomised greedy algorithm for finding a small CDS of regular graphs. We analyse the average-case performance of this heuristic on random regular graphs using differential equations. In this way we prove an upper bound on the size of a minimum CDS of random regular graphs.
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Duckworth, W., Mans, B. (2002). On the Connected Domination Number of Random Regular Graphs. In: Ibarra, O.H., Zhang, L. (eds) Computing and Combinatorics. COCOON 2002. Lecture Notes in Computer Science, vol 2387. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45655-4_24
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DOI: https://doi.org/10.1007/3-540-45655-4_24
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