{"paper":{"title":"On Leighton's graph covering theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Walter D. Neumann","submitted_at":"2009-06-13T19:10:16Z","abstract_excerpt":"We give short expositions of both Leighton's proof and the Bass-Kulkarni proof of Leighton's graph covering theorem, in the context of colored graphs. We discuss a further generalization, needed elsewhere, to \"symmetry-restricted graphs.\" We can prove it in some cases, for example, if the \"graph of colors\" is a tree, but we do not know if it is true in general. We show that Bass's Conjugation Theorem, which is a tool in the Bass-Kulkarni approach, does hold in the symmetry-restricted context."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.2496","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"}