{"paper":{"title":"On saturation games","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alon Naor, Dan Hefetz, Michael Krivelevich, Milo\\v{s} Stojakovi\\'c","submitted_at":"2014-06-09T09:03:10Z","abstract_excerpt":"A graph $G = (V,E)$ is said to be saturated with respect to a monotone increasing graph property ${\\mathcal P}$, if $G \\notin {\\mathcal P}$ but $G \\cup \\{e\\} \\in {\\mathcal P}$ for every $e \\in \\binom{V}{2} \\setminus E$. The saturation game $(n, {\\mathcal P})$ is played as follows. Two players, called Mini and Max, progressively build a graph $G \\subseteq K_n$, which does not satisfy ${\\mathcal P}$. Starting with the empty graph on $n$ vertices, the two players take turns adding edges $e \\in \\binom{V(K_n)}{2} \\setminus E(G)$, for which $G \\cup \\{e\\} \\notin {\\mathcal P}$, until no such edge exis"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.2111","kind":"arxiv","version":3},"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"}