{"paper":{"title":"Fat Hoffman graphs with smallest eigenvalue at least $-1-\\tau$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Akihiro Munemasa, Tetsuji Taniguchi, Yoshio Sano","submitted_at":"2011-11-30T19:35:31Z","abstract_excerpt":"In this paper, we show that all fat Hoffman graphs with smallest eigenvalue at least -1-\\tau, where \\tau is the golden ratio, can be described by a finite set of fat (-1-\\tau)-irreducible Hoffman graphs. In the terminology of Woo and Neumaier, we mean that every fat Hoffman graph with smallest eigenvalue at least -1-\\tau is an H-line graph, where H is the set of isomorphism classes of maximal fat (-1-\\tau)-irreducible Hoffman graphs. It turns out that there are 37 fat (-1-\\tau)-irreducible Hoffman graphs, up to isomorphism."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.7284","kind":"arxiv","version":4},"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"}