On the Connected Domination Number of Random Regular Graphs

Authors:
William Duckworth;Bernard Mans
Affiliations:
-;-
Venue:
COCOON '02 Proceedings of the 8th Annual International Conference on Computing and Combinatorics
Year:
2002

Citing 4
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Abstract

A connected dominating set (CDS) of a graph, G, is a set of vertices, C 驴 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.