### 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 - Mar 2013 |

Externally published | Yes |

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### All Science Journal Classification (ASJC) codes

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

### Cite this

*IEICE Transactions on Information and Systems*,

*E96-D*(3), 443-449. https://doi.org/10.1587/transinf.E96.D.443

**Inapproximability of maximum r-regular induced connected subgraph problems.** / Asahiro, Yuichi; Eto, Hiroshi; Miyano, Eiji.

Research output: Contribution to journal › Article

*IEICE Transactions on Information and Systems*, vol. E96-D, no. 3, pp. 443-449. https://doi.org/10.1587/transinf.E96.D.443

}

TY - JOUR

T1 - Inapproximability of maximum r-regular induced connected subgraph problems

AU - Asahiro, Yuichi

AU - Eto, Hiroshi

AU - Miyano, Eiji

PY - 2013/3

Y1 - 2013/3

N2 - 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 n1-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 n1/6-ε in polynomial time for any ε > 0 unless P = NP.

AB - 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 n1-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 n1/6-ε in polynomial time for any ε > 0 unless P = NP.

UR - http://www.scopus.com/inward/record.url?scp=84878238046&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84878238046&partnerID=8YFLogxK

U2 - 10.1587/transinf.E96.D.443

DO - 10.1587/transinf.E96.D.443

M3 - Article

AN - SCOPUS:84878238046

VL - E96-D

SP - 443

EP - 449

JO - IEICE Transactions on Information and Systems

JF - IEICE Transactions on Information and Systems

SN - 0916-8532

IS - 3

ER -