### Abstract

We study the problem of finding a maximum vertex-subset S of a given graph G such that the subgraph G[S] induced by S is r-regular for a prescribed degree r ≥ 0. We also consider a variant of the problem which requires G[S] to be r-regular and connected. Both problems are known to be NP-hard even to approximate for a fixed constant r. In this paper, we thus consider the problems whose input graphs are restricted to some special classes of graphs. We first show that the problems are still NP-hard to approximate even if r is a fixed constant and the input graph is either bipartite or planar. On the other hand, both problems are tractable for graphs having tree-like structures, as follows. We give linear-time algorithms to solve the problems for graphs with bounded treewidth; we note that the hidden constant factor of our running time is just a single exponential of the treewidth. Furthermore, both problems are solvable in polynomial time for chordal graphs.

Original language | English |
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Title of host publication | Fundamentals of Computation Theory - 19th International Symposium, FCT 2013, Proceedings |

Pages | 28-39 |

Number of pages | 12 |

DOIs | |

Publication status | Published - Sep 3 2013 |

Externally published | Yes |

Event | 19th International Symposium on Fundamentals of Computation Theory, FCT 2013 - Liverpool, United Kingdom Duration: Aug 19 2013 → Aug 21 2013 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 8070 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 19th International Symposium on Fundamentals of Computation Theory, FCT 2013 |
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Country | United Kingdom |

City | Liverpool |

Period | 8/19/13 → 8/21/13 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Fundamentals of Computation Theory - 19th International Symposium, FCT 2013, Proceedings*(pp. 28-39). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8070 LNCS). https://doi.org/10.1007/978-3-642-40164-0_6