{"paper":{"title":"Multidesigns for a graph pair of order 6","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dan Roberts, Yizhe Gao","submitted_at":"2017-05-26T16:21:48Z","abstract_excerpt":"Given two graphs $G$ and $H$, a $(G,H)$-multidecomposition of $K_{n}$ is a partition of the edges of $K_{n}$ into copies of $G$ and $H$ such that at least one copy of each is used. We give necessary and sufficient conditions for the existence of $(C_{6},\\overline{C}_{6})$-multidecomposition of $K_{n}$ where $C_{6}$ denotes a cycle of length 6 and $\\overline{C}_{6}$ denotes the complement of $C_{6}$.\n  A $(G,H)$-multipacking of $K_{n}$ is a partition of a subset of the edges of $K_{n}$ into copies of $G$ and $H$ such that at least one copy of each is used. The set consisting of the edges of $K_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.09638","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"}