{"paper":{"title":"Non-reconstructible locally finite graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Florian Lehner, Joshua Erde, Max Pitz, Nathan Bowler, Peter Heinig","submitted_at":"2016-11-14T12:59:35Z","abstract_excerpt":"Two graphs $G$ and $H$ are \\emph{hypomorphic} if there exists a bijection $\\varphi \\colon V(G) \\rightarrow V(H)$ such that $G - v \\cong H - \\varphi(v)$ for each $v \\in V(G)$. A graph $G$ is \\emph{reconstructible} if $H \\cong G$ for all $H$ hypomorphic to $G$.\n  Nash-Williams proved that all locally finite graphs with a finite number $\\geq 2$ of ends are reconstructible, and asked whether locally finite graphs with one end or countably many ends are also reconstructible.\n  In this paper we construct non-reconstructible graphs of bounded maximum degree with one and countably many ends respective"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.04370","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"}