{"paper":{"title":"Cyclic hamiltonian cycle systems of the complete multipartite graph: even number of parts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Anita Pasotti, Francesca Merola, Marco Antonio Pellegrini","submitted_at":"2015-04-28T07:57:15Z","abstract_excerpt":"A hamiltonian cycle system (HCS, for short) of a graph $\\Gamma$ is a partition of the edges of $\\Gamma$ into hamiltonian cycles. A HCS is cyclic when it is invariant under a cyclic permutation of all the vertices of $\\Gamma$; the existence problem for a cyclic HCS has been completely solved by Buratti and Del Fra in 2004 when $\\Gamma$ is the complete graph $K_v$, $v$ odd, and by Jordon and Morris in 2008 when $\\Gamma$ is the complete graph minus a $1$-factor $K_v-I$, $v$ even. In this work we present a complete solution to the existence problem of a cyclic HCS for $\\Gamma = K_{m\\times n}$, the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.07369","kind":"arxiv","version":1},"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"}