## Abstract

In this article we provide hardness results and approximation algorithms for the following three natural degree-constrained subgraph problems, which take as input an undirected graph G=(V,E). Let d<2 be a fixed integer. The Maximumd-degree-bounded Connected Subgraph (MDBCSd) problem takes as additional input a weight function ω:E→R+, and asks for a subset E′⊆E such that the subgraph induced by E′ is connected, has maximum degree at most d, and ∑e∈E′ω(e) is maximized. The Minimum Subgraph of Minimum Degree<d (MSMDd) problem involves finding a smallest subgraph of G with minimum degree at least d. Finally, the Dual Degree-densek-Subgraph (DDDkS) problem consists in finding a subgraph H of G such that |V(H)|≤k and the minimum degree in H is maximized.

Original language | English |
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Pages (from-to) | 1661-1679 |

Number of pages | 19 |

Journal | Discrete Applied Mathematics |

Volume | 160 |

Issue number | 12 |

DOIs | |

State | Published - Aug 2012 |

Externally published | Yes |

## Keywords

- Approximation algorithms
- Degree-constrained subgraph
- Hardness of approximation