{"paper":{"title":"Monochromatic Clique Decompositions of Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Henry Liu, Oleg Pikhurko, Teresa Sousa","submitted_at":"2014-01-24T14:30:29Z","abstract_excerpt":"Let $G$ be a graph whose edges are coloured with $k$ colours, and $\\mathcal H=(H_1,\\dots , H_k)$ be a $k$-tuple of graphs. A monochromatic $\\mathcal H$-decomposition of $G$ is a partition of the edge set of $G$ such that each part is either a single edge or forms a monochromatic copy of $H_i$ in colour $i$, for some $1\\le i\\le k$. Let $\\phi_{k}(n,\\mathcal H)$ be the smallest number $\\phi$, such that, for every order-$n$ graph and every $k$-edge-colouring, there is a monochromatic $\\mathcal H$-decomposition with at most $\\phi$ elements. Extending the previous results of Liu and Sousa [\"Monochro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.6345","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"}