{"paper":{"title":"Almost 2-perfect 8-cycle systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Charles Curtis Lindner, Emine \\c{S}ule Yaz{\\i}c{\\i}, Selda K\\\"u\\c{c}\\\"uk\\c{c}if\\c{c}i, Sibel \\\"Ozkan","submitted_at":"2017-10-23T13:40:05Z","abstract_excerpt":"For an $m$-cycle $C$, an inside $m$-cycle of $C$ is a cycle on the same vertex set, that is edge-disjoint from $C$. In an $m$-cycle system, $(\\mathcal{X}, \\mathcal{C})$, if inside $m$-cycles can be chosen -one for each cycle- to form another $m$-cycle system, then $(\\mathcal{X}, \\mathcal{C})$ is called an almost $2$-perfect $m$-cycle system. Almost $2$-perfect cycle systems can be considered as generalisations of $2$-perfect cycle systems. Cycle packings are generalisations of cycle systems that allow to have leaves after decomposition. In this paper, we prove that an almost $2$-perfect maximu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.08265","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"}