{"paper":{"title":"Monochromatic bounded degree subgraph partitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Andrey Grinshpun, Gabor N. Sarkozy","submitted_at":"2014-05-29T09:35:24Z","abstract_excerpt":"Let ${\\cal{F}}=\\{F_1,F_2,\\ldots\\}$ be a sequence of graphs such that $F_n$ is a graph on $n$ vertices with maximum degree at most $\\Delta$. We show that there exists an absolute constant $C$ such that the vertices of any 2-edge-colored complete graph can be partitioned into at most $2^{C\\Delta \\log{\\Delta}}$ vertex disjoint monochromatic copies of graphs from ${\\cal{F}}$. If each $F_n$ is bipartite, then we can improve this bound to $2^{C \\Delta}$; this result is optimal up to the constant $C$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.7507","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"}