## Abstract

Given a connected graph G = (V, E) on n vertices, the Maximum r-Regular Induced Connected Subgraph (r-MaxRICS) problem asks for a maximum sized subset of vertices S ⊆ V such that the induced subgraph G[S] on S is connected and r-regular. It is known that 2-MaxRICS and 3-MaxRICS are NP-hard. Moreover, 2-MaxRICS cannot be approximated within a factor of n^{1-ε} in polynomial time for any ε > 0 unless P = NP. In this paper, we show that r-MaxRICS are NP-hard for any fixed integer r ≥ 4. Furthermore, we show that for any fixed integer r ≥ 3, r-MaxRICS cannot be approximated within a factor of n^{1/6-ε} in polynomial time for any ε > 0 unless P = NP.

Original language | English |
---|---|

Pages (from-to) | 443-449 |

Number of pages | 7 |

Journal | IEICE Transactions on Information and Systems |

Volume | E96-D |

Issue number | 3 |

DOIs | |

Publication status | Published - 2013 Mar |

Externally published | Yes |

## Keywords

- Inapproximability
- Induced connected subgraph
- NP-hardness
- Regularity

## ASJC Scopus subject areas

- Software
- Hardware and Architecture
- Computer Vision and Pattern Recognition
- Electrical and Electronic Engineering
- Artificial Intelligence