{"paper":{"title":"The Hamilton-Waterloo Problem with even cycle lengths","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"A.C. Burgess, P. Danziger, T. Traetta","submitted_at":"2018-10-04T00:11:19Z","abstract_excerpt":"The Hamilton-Waterloo Problem HWP$(v;m,n;\\alpha,\\beta)$ asks for a 2-factorization of the complete graph $K_v$ or $K_v-I$, the complete graph with the edges of a 1-factor removed, into $\\alpha$ $C_m$-factors and $\\beta$ $C_n$-factors, where $3 \\leq m < n$. In the case that $m$ and $n$ are both even, the problem has been solved except possibly when $1 \\in \\{\\alpha,\\beta\\}$ or when $\\alpha$ and $\\beta$ are both odd, in which case necessarily $v \\equiv 2 \\pmod{4}$. In this paper, we develop a new construction that creates factorizations with larger cycles from existing factorizations under certai"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.02009","kind":"arxiv","version":3},"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"}