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On the Connected Domination Number of Random Regular Graphs

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Computing and Combinatorics (COCOON 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2387))

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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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Author information

Authors and Affiliations

  1. Department of Computing, Macquarie University, Sydney, NSW, 2109, Australia

    William Duckworth & Bernard Mans

Authors
  1. William Duckworth
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  2. Bernard Mans
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of California, Santa Barbara, California, 93106, USA

    Oscar H. Ibarra

  2. Department of Mathematics, National University of Singapore, Singapore, Singapore, 117543

    Louxin Zhang

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© 2002 Springer-Verlag Berlin Heidelberg

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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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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43996-7

  • Online ISBN: 978-3-540-45655-1

  • eBook Packages: Springer Book Archive

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