2016/10/20 by Ross J. Kang, Kang, Ross, Viresh Patel +3
Computer Science · Mathematics · #05C55 (Primary) #05D10 #05D40 (Secondary) #Advanced Topology and Set Theory #Combinatorics (math.CO) #Digital Image Processing Techniques #FOS: Mathematics #Limits and Structures in Graph Theory
paper · doi:10.48550/arxiv.1610.06359
openalex publication_date 2016/10/20 · openalex created_date 2019/07/30 · openalex updated_date 2026/07/28
Erdős and Pach (1983) introduced the natural degree-based generalisations of Ramsey numbers, where instead of seeking large monochromatic cliques in a 2-edge coloured complete graph, we seek monochromatic subgraphs of high minimum or average degree. Here we expand the study of these so-called quasi-Ramsey numbers in a few ways, in particular, to multiple colours and to uniform hypergraphs. Quasi-Ramsey numbers are known to exhibit a certain unique phase transition and we show that this is also the case across the settings we consider. Our results depend on a density-biased notion of hypergraph discrepancy optimised over sets of bounded size, which may be of independent interest.