{"paper":{"title":"Fixing improper colorings of graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Konstanty Junosza-Szaniawski, Mathieu Liedloff, Pawe{\\l} Rz\\k{a}\\.zewski, Pedro Montealegre, Valentin Garnero","submitted_at":"2016-07-23T10:09:56Z","abstract_excerpt":"In this paper we consider a variation of a recoloring problem, called the Color-Fixing. Let us have some non-proper $r$-coloring $\\varphi$ of a graph $G$. We investigate the problem of finding a proper $r$-coloring of $G$, which is \"the most similar\" to $\\varphi$, i.e. the number $k$ of vertices that have to be recolored is minimum possible. We observe that the problem is NP-complete for any $r \\geq 3$, even for bipartite planar graphs. On the other hand, the problem is fixed-parameter tractable, when parameterized by the number of allowed transformations $k$. We provide an $2^n \\cdot n^{\\math"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.06911","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":""},"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"}