## Abstract

We study the problem of deleting the smallest set S of vertices (resp. edges) from a given graph G such that the induced subgraph (resp. subgraph) G\S belongs to some class H. We consider the case where graphs in H have treewidth bounded by t, and give a general framework to obtain approximation algorithms for both vertex and edge-deletion settings from approximation algorithms for certain natural graph partitioning problems called k-Subset Vertex Separator and k-Subset Edge Separator, respectively. For the vertex deletion setting, our framework combined with the current best result for k-Subset Vertex Separator, improves approximation ratios for basic problems such as k-Treewidth Vertex Deletion and Planar-F Vertex Deletion. Our algorithms are simpler than previous works and give the first deterministic and uniform approximation algorithms under the natural parameterization. For the edge deletion setting, we give improved approximation algorithms for k-Subset Edge Separator combining ideas from LP relaxations and important separators. We present their applications in bounded-degree graphs, and also give an APX-hardness result for the edge deletion problems.

Original language | English |
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Pages | 1731-1749 |

Number of pages | 19 |

DOIs | |

State | Published - 1 Jan 2019 |

Externally published | Yes |

Event | 30th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2019 - San Diego, United States Duration: 6 Jan 2019 → 9 Jan 2019 |

### Conference

Conference | 30th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2019 |
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Country/Territory | United States |

City | San Diego |

Period | 6/01/19 → 9/01/19 |

## ASJC Scopus subject areas

- Software
- General Mathematics