{"paper":{"title":"$H$-Decomposition of $r$-graphs when $H$ is an $r$-graph with exactly $k$ independent edges","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Boyuan Liu, Hongliang Lu, Xinmin Hou","submitted_at":"2017-10-15T15:30:28Z","abstract_excerpt":"Let $\\phi_H^r(n)$ be the smallest integer such that, for all $r$-graphs $G$ on $n$ vertices, the edge set $E(G)$ can be partitioned into at most $\\phi_H^r(n)$ parts, of which every part either is a single edge or forms an $r$-graph isomorphic to $H$. The function $\\phi^2_H(n)$ has been well studied in literature, but for the case $r\\ge 3$, the problem that determining the value of $\\phi_H^r(n)$ is widely open. Sousa (2010) gave an asymptotic value of $\\phi_H^r(n)$ when $H$ is an $r$-graph with exactly 2 edges, and determined the exact value of $\\phi_H^r(n)$ in some special cases. In this paper"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.05347","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"}