## Abstract

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 γ_{2}(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 thatγ_{2}(G)≤n lnδ(G)/δ(G) (1+o_{δ}(1)) where o_{δ}(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 language | English |
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Pages (from-to) | 265-271 |

Number of pages | 7 |

Journal | Discrete Mathematics |

Volume | 269 |

Issue number | 1-3 |

DOIs | |

State | Published - 28 Jul 2003 |

## Keywords

- Connectivity
- Domination
- Minimum degree

## ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics