{"paper":{"title":"An Algorithmic Meta-Theorem for Graph Modification to Planarity and FOL","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM","cs.LO"],"primary_cat":"cs.DS","authors_text":"Dimitrios M. Thilikos, Fedor V. Fomin, Giannos Stamoulis, Petr A. Golovach","submitted_at":"2021-06-07T08:44:25Z","abstract_excerpt":"In general, a graph modification problem is defined by a graph modification operation $\\boxtimes$ and a target graph property ${\\cal P}$. Typically, the modification operation $\\boxtimes$ may be vertex removal}, edge removal}, edge contraction}, or edge addition and the question is, given a graph $G$ and an integer $k$, whether it is possible to transform $G$ to a graph in ${\\cal P}$ after applying $k$ times the operation $\\boxtimes$ on $G$. This problem has been extensively studied for particilar instantiations of $\\boxtimes$ and ${\\cal P}$. In this paper we consider the general property ${\\c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.03425","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2106.03425/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}