{"paper":{"title":"Domination game on forests","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Csilla Bujt\\'as","submitted_at":"2014-04-04T20:04:12Z","abstract_excerpt":"In the domination game studied here, Dominator and Staller alternately choose a vertex of a graph $G$ and take it into a set $D$. The number of vertices dominated by the set $D$ must increase in each single turn and the game ends when $D$ becomes a dominating set of $G$. Dominator aims to minimize whilst Staller aims to maximize the number of turns (or equivalently, the size of the dominating set $D$ obtained at the end). Assuming that Dominator starts and both players play optimally, the number of turns is called the game domination number $\\gamma_g(G)$ of $G$.\n  Kinnersley, West and Zamani v"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.1382","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"}