{"paper":{"title":"Waiter-Client and Client-Waiter Hamiltonicity games on random graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dan Hefetz, Michael Krivelevich, Wei En Tan","submitted_at":"2015-09-17T18:19:32Z","abstract_excerpt":"We study two types of two player, perfect information games with no chance moves, played on the edge set of the binomial random graph ${\\mathcal G}(n,p)$. In each round of the $(1 : q)$ Waiter-Client Hamiltonicity game, the first player, called Waiter, offers the second player, called Client, $q+1$ edges of ${\\mathcal G}(n,p)$ which have not been offered previously. Client then chooses one of these edges, which he claims, and the remaining $q$ edges go back to Waiter. Waiter wins this game if by the time every edge of ${\\mathcal G}(n,p)$ has been claimed by some player, the graph consisting of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.05356","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"}