{"paper":{"title":"Simple cubic graphs with no short traveling salesman tour","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"J\\'an Maz\\'ak, Robert Luko\\v{t}ka","submitted_at":"2017-12-29T10:30:11Z","abstract_excerpt":"Let $tsp(G)$ denote the length of a shortest travelling salesman tour in a graph $G$. We prove that for any $\\varepsilon>0$, there exists a simple $2$-connected planar cubic graph $G_1$ such that $tsp(G_1)\\ge (1.25-\\varepsilon)\\cdot|V(G_1)|$, a simple $2$-connected bipartite cubic graph $G_2$ such that $tsp(G_2)\\ge (1.2-\\varepsilon)\\cdot|V(G_2)|$, and a simple $3$-connected cubic graph $G_3$ such that $tsp(G_3)\\ge (1.125-\\varepsilon)\\cdot|V(G_3)|$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.10167","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"}