2016/01/31 by David Conlon, Domingos Dellamonica, Domingos Dellamonica Jr. +3 · 1 citation
Computer Science · Mathematics · #Advanced Graph Theory Research #Advanced Topology and Set Theory #Bounded function #Combinatorics #Discrete mathematics #Function (biology) #Graph #Hypergraph #Limits and Structures in Graph Theory #Mathematics #Monochromatic color #Natural number #Physics #Ramsey theory #Ramsey's theorem #math.CO
paper · pdf · doi:10.1007/978-3-319-44479-6_13
published as A Journey Through Discrete Mathematics (A Tribute to Jiří Matoušek), Springer, 2017, 357-366 · Dedicated to the memory of Jirka Matoušek, 10 pages, second version addresses changes arising from the referee reports
arxiv created 2016/06/24 · crossref issued 2017/01/01 · crossref published 2017/01/01 · crossref published-print 2017/01/01 · openalex publication_date 2017/01/01 · crossref published-online 2017/05/09 · crossref created 2017/10/10 · arxiv updated 2017/11/01 · crossref deposited 2020/10/19 · crossref indexed 2025/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The induced Ramsey number rind(F) of a k-uniform hypergraph F is the smallest natural number n for which there exists a k-uniform hypergraph G on n vertices such that every two-coloring of the edges of G contains an induced monochromatic copy of F. We study this function, showing that rind(F) is bounded above by a reasonable power of r(F). In particular, our result implies that rind(F) ≤ 2^2ct for any 3-uniform hypergraph F with t vertices, mirroring the best known bound for the usual Ramsey number. The proof relies on an application of the hypergraph container method.