{"paper":{"title":"The Game Saturation Number of a Graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Benjamin Reiniger, Douglas B. West, James M. Carraher, William B. Kinnersley","submitted_at":"2014-05-12T16:55:16Z","abstract_excerpt":"Given a family ${\\mathcal F}$ and a host graph $H$, a graph $G\\subseteq H$ is ${\\mathcal F}$-saturated relative to $H$ if no subgraph of $G$ lies in ${\\mathcal F}$ but adding any edge from $E(H)-E(G)$ to $G$ creates such a subgraph. In the ${\\mathcal F}$-saturation game on $H$, players Max and Min alternately add edges of $H$ to $G$, avoiding subgraphs in ${\\mathcal F}$, until $G$ becomes ${\\mathcal F}$-saturated relative to $H$. They aim to maximize or minimize the length of the game, respectively; $\\textrm{sat}_g({\\mathcal F};H)$ denotes the length under optimal play (when Max starts).\n  Let"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.2834","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"}