{"paper":{"title":"On the Complexity of the Mis\\`ere Version of Three Games Played on Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Gabriel Renault, Simon Schmidt","submitted_at":"2014-01-02T09:43:40Z","abstract_excerpt":"We investigate the complexity of finding a winning strategy for the mis\\`ere version of three games played on graphs : two variants of the game $\\text{NimG}$, introduced by Stockmann in 2004 and the game $\\text{Vertex Geography}$ on both directed and undirected graphs. We show that on general graphs those three games are $\\text{PSPACE}$-Hard or Complete. For one $\\text{PSPACE}$-Hard variant of $\\text{NimG}$, we find an algorithm to compute an effective winning strategy in time $\\mathcal{O}(\\sqrt{|V(G)|}.|E(G)|)$ when $G$ is a bipartite graph."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.0400","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"}