2014/11/24 by Natasha Dobrinen, Dobrinen, Natasha, Claude Laflamme +3
Computer Science · Mathematics · #03C13 #03C15 #03C99 #05C17 #05C55 #Advanced Topology and Set Theory #Combinatorics (math.CO) #Computability, Logic, AI Algorithms #FOS: Mathematics #Limits and Structures in Graph Theory #Logic (math.LO) #math.CO #math.LO #msc:03C13 #msc:03C15 #msc:03C99 #msc:05C17 #msc:05C55
paper · pdf · doi:10.48550/arxiv.1411.6678
12 pages
arxiv created 2014/11/24 · openalex publication_date 2014/11/24 · arxiv updated 2014/11/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A relational structure R is \em rainbow Ramsey if for every finite induced substructure C of R and every colouring of the copies of C with countably many colours, such that each colour is used at most k times for a fixed k, there exists a copy R^∗ of R so that the copies of C in R^∗ use each colour at most once. We show that certain ultrahomogenous binary relational structures, for example the Rado graph, are rainbow Ramsey. Via compactness this then implies that for all finite graphs B and C and k ∈ ω, there exists a graph A so that for every colouring of the copies of C in A such that each colour is used at most k times, there exists a copy B^∗ of B in A so that the copies of C in B^∗ use each colour at most once.