## Abstract

The elimination distance to some target graph property P is a general graph modification parameter introduced by Bulian and Dawar. We initiate the study of elimination distances to graph properties expressible in first-order logic. We delimit the problem's fixed-parameter tractability by identifying sufficient and necessary conditions on the structure of prefixes of first-order logic formulas. Our main result is the following meta-theorem: For every graph property P expressible by a first order-logic formula , that is, of the form where is a quantifier-free first-order formula, checking whether the elimination distance of a graph to P does not exceed , is fixed-parameter tractable parameterized by . Properties of graphs expressible by formulas from include being of bounded degree, excluding a forbidden subgraph, or containing a bounded dominating set. We complement this theorem by showing that such a general statement does not hold for formulas with even slightly more expressive prefix structure: There are formulas , for which computing elimination distance is -hard.

Original language | English (US) |
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Article number | 17 |

Journal | ACM Transactions on Computational Logic |

Volume | 23 |

Issue number | 3 |

DOIs | |

State | Published - Jul 2022 |

## Keywords

- descriptive complexity
- elimination distance
- First-order logic
- parameterized complexity

## ASJC Scopus subject areas

- Theoretical Computer Science
- General Computer Science
- Logic
- Computational Mathematics