{"paper":{"title":"On the connectivity Waiter-Client game","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Codru\\u{t} Grosu, Lothar Narins, Sylwia Antoniuk","submitted_at":"2015-10-20T12:13:29Z","abstract_excerpt":"In this short note we consider a variation of the connectivity Waiter-Client game $WC(n,q,\\mathcal{A})$ played on an $n$-vertex graph $G$ which consists of $q+1$ disjoint spanning trees. In this game in each round Waiter offers Client $q+1$ edges of $G$ which have not yet been offered. Client chooses one edge and the remaining $q$ edges are discarded. The aim of Waiter is to force Client to build a connected graph. If this happens Waiter wins. Otherwise Client is the winner. We consider the case where $2 < q+1 < \\lfloor \\frac{n-1}{2}\\rfloor$ and show that for each such $q$ there exists a graph"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.05852","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"}