## Abstract

Given an undirected graph and an integer q, the Edge Cover problem asks for a subgraph with at most q edges such that each vertex has degree at least one. We show NP-hardness of two generalizations of the Edge Cover problem, which were conjectured to be polynomial-time solvable, solving three open questions from computational social choice. Both generalizations introduce weights on the edges and an individual demand b(v) for each vertex v. The first generalization, named Simple b-Edge Weighted Cover, requires the edge set to have a total weight of at most q while each vertex v is to be adjacent to at least b(v) edges. The second generalization, named Simple Weighted b-Edge Cover, requires the edge set to contain at most q edges while each vertex v is to be adjacent to edges of total weight at least b(v).

Original language | English |
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Pages (from-to) | 147-152 |

Number of pages | 6 |

Journal | Information Processing Letters |

Volume | 116 |

Issue number | 2 |

DOIs | |

State | Published - 1 Feb 2016 |

Externally published | Yes |

## Keywords

- Approval voting
- Computational complexity
- Computational social choice
- Graph problems
- Manipulating elections

## ASJC Scopus subject areas

- Theoretical Computer Science
- Signal Processing
- Information Systems
- Computer Science Applications