Connected domination and spanning trees with many leaves

Yair Caro, Douglas B. West, Raphael Yuster

Research output: Contribution to journalArticlepeer-review


Let G = (V, E) be a connected graph. A connected dominating set S ⊂ V is a dominating set that induces a connected subgraph of G. The connected domination number of G, denoted γc(G), is the minimum cardinality of a connected dominating set. Alternatively, |V| - γc(G) is the maximum number of leaves in a spanning tree of G. Let δ denote the minimum degree of G. We prove that γc(G) ≤ |V| ln(δ+1)/δ+1 (1 + oδ(1)). Two algorithms that construct a set this good are presented. One is a sequential polynomial time algorithm, while the other is a randomized parallel algorithm in RNC.

Original languageEnglish
Pages (from-to)202-211
Number of pages10
JournalSIAM Journal on Discrete Mathematics
Issue number2
StatePublished - Apr 2000


  • Connectivity
  • Domination
  • Spanning trees

ASJC Scopus subject areas

  • General Mathematics


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