{"paper":{"title":"On the existence of unparalleled even cycle systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Eric Mendelsohn, Peter Danziger, Tommaso Traetta","submitted_at":"2015-10-23T22:56:20Z","abstract_excerpt":"A $2t$-cycle system of order $v$ is a set $\\mathcal{C}$ of cycles whose edges partition the edge-set of $K_v-I$ (i.e., the complete graph minus the $1$-factor $I$). If $v\\equiv 0 \\pmod{2t}$, a set of $v/2t$ vertex-disjoint cycles of $\\mathcal{C}$ is a parallel class. If $\\mathcal{C}$ has no parallel classes, we call such a system unparalleled.\n  We show that there exists an unparalleled $2t$-cycle system of order $v \\equiv 0 \\pmod{2t}$ if and only if $v>2t>2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.07082","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"}