{"paper":{"title":"On bipartite graphs of defect at most 4","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"(2) Centre for Informatics, Applied Optimization, Australia, Australia), Computer Science, Guillermo Pineda-Villavicencio (2) ((1) School of Electrical Engineering, Ramiro Feria-Pur\\'on (1), The University of Newcastle, University of Ballarat","submitted_at":"2010-10-27T11:31:09Z","abstract_excerpt":"We consider the bipartite version of the degree/diameter problem, namely, given natural numbers {\\Delta} \\geq 2 and D \\geq 2, find the maximum number Nb({\\Delta},D) of vertices in a bipartite graph of maximum degree {\\Delta} and diameter D. In this context, the Moore bipartite bound Mb({\\Delta},D) represents an upper bound for Nb({\\Delta},D). Bipartite graphs of maximum degree {\\Delta}, diameter D and order Mb({\\Delta},D), called Moore bipartite graphs, have turned out to be very rare. Therefore, it is very interesting to investigate bipartite graphs of maximum degree {\\Delta} \\geq 2, diameter"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.5651","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"}