{"paper":{"title":"The Graph Coloring Game on $4\\times n$-Grids","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Caroline Brosse, Nicolas Martins, Nicolas Nisse, Rudini Sampaio","submitted_at":"2024-12-23T15:54:14Z","abstract_excerpt":"The graph coloring game is a famous two-player game (re)introduced by Bodlaender in $1991$. Given a graph $G$ and $k \\in \\mathbb{N}$, Alice and Bob alternately (starting with Alice) color an uncolored vertex with some color in $\\{1,\\cdots,k\\}$ such that no two adjacent vertices receive a same color. If eventually all vertices are colored, then Alice wins and Bob wins otherwise. The game chromatic number $\\chi_g(G)$ is the smallest integer $k$ such that Alice has a winning strategy with $k$ colors in $G$. It has been recently (2020) shown that, given a graph $G$ and $k\\in \\mathbb{N}$, deciding "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.17668","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.17668/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"}