{"paper":{"title":"FPT Algorithms for Conflict-free Coloring of Graphs and Chromatic Terrain Guarding","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.CG"],"primary_cat":"cs.DS","authors_text":"Akanksha Agrawal, Dolly Yadav, Meghana M Reddy, Pradeesha Ashok, Saket Saurabh","submitted_at":"2019-05-06T04:29:28Z","abstract_excerpt":"We present fixed parameter tractable algorithms for the conflict-free coloring problem on graphs. Given a graph $G=(V,E)$, \\emph{conflict-free coloring} of $G$ refers to coloring a subset of $V$ such that for every vertex $v$, there is a color that is assigned to exactly one vertex in the closed neighborhood of $v$. The \\emph{k-Conflict-free Coloring} problem is to decide whether $G$ can be conflict-free colored using at most $k$ colors. This problem is NP-hard even for $k=1$ and therefore under standard complexity theoretic assumptions, FPT algorithms do not exist when parameterised by the so"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.01822","kind":"arxiv","version":1},"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"}