2-connected graphs with small 2-connected dominating sets

Yair Caro, Raphael Yuster

Research output: Contribution to journalArticlepeer-review


Let G be a 2-connected graph. A subset D of V(G) is a 2-connected dominating set if every vertex of G has a neighbor in D and D induces a 2-connected subgraph. Let γ2(G) denote the minimum size of a 2-connected dominating set of G. Let δ(G) be the minimum degree of G. For an n-vertex graph G, we prove thatγ2(G)≤n lnδ(G)/δ(G) (1+oδ(1)) where oδ(1) denotes a function that tends to 0 as δ→∞. The upper bound is asymptotically tight. This extends the results in (Arnautov, Prikl. Mat. i Programmirovanie 11 (1974) 3-8, Caro et al., SIAM J. Discrete Math. 13 (2000) 202-211, Lovász, Discrete Math. 13 (1975) 383-390 and Payan, Cahièrs Centre Etudes Rech. Opér. 17 (1975) 307-317).

Original languageEnglish
Pages (from-to)265-271
Number of pages7
JournalDiscrete Mathematics
Issue number1-3
StatePublished - 28 Jul 2003


  • Connectivity
  • Domination
  • Minimum degree

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics


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