{"paper":{"title":"A Classification of Orientable Regular Embeddings of Complete Multipartite Graphs","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Junyang Zhang, Shaofei Du","submitted_at":"2012-02-09T13:22:33Z","abstract_excerpt":"Let $K_{m[n]}$ be the complete multipartite graph with $m$ parts, while each part contains $n$ vertices. The orientably-regular embeddings of complete graphs $K_{m[1]}$ have been determined by Biggs (1971) \\cite{Big1}, James and Jones (1985) \\cite{JJ}. During the past twenty years, several papers such as Du et al.(2007, 2010) \\cite{DJKNS1,DJKNS2}, Jones et al. (2007, 2008) \\cite{JNS1,JNS2}, Kwak and Kwon (2005, 2008) \\cite{KK1,KK2} and Nedela et al. (1997, 2002)\\cite{NS,NSZ} contributed to the orientably-regular embeddings of complete bipartite graphs $K_{2[n]}$ and the final classification wa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.1974","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"}