{"paper":{"title":"The Hamilton-Waterloo Problem with $C_4$ and $C_m$ Factors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Sibel \\\"Ozkan, U\\u{g}ur Odaba\\c{s}{\\i}","submitted_at":"2015-05-29T17:43:15Z","abstract_excerpt":"The Hamilton-Waterloo problem with uniform cycle sizes asks for a $2-$ factorization of the complete graph $K_v$ (for odd {\\em v}) or $K_v$ minus a $1-$factor (for even {\\em v}) where $r$ of the factors consist of $n-$cycles and $s$ of the factors consist of $m-$cycles with $r+s=\\left \\lfloor \\frac{v-1}{2} \\right \\rfloor$. In this paper, the Hamilton-Waterloo Problem with $4-$cycle and $m-$cycle factors for odd $m\\geq 3$ is studied and all possible solutions with a few possible exceptions are determined."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.08121","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"}