2021/09/20 by António Girão, Oliver Janzer, Girão, António +1
Materials Science · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Limits and Structures in Graph Theory #Quasicrystal Structures and Properties
paper · pdf · doi:10.48550/arxiv.2109.09642
openalex publication_date 2021/09/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that for any r∈ ℕ, there exists a constant Cr such that the following is true. Let F=\F1,F2,…\ be an infinite sequence of bipartite graphs such that |V(Fi)|=i and Δ(Fi)≤ Δ hold for all i. Then in any r-edge coloured complete graph Kn, there is a collection of at most exp(CrΔ) monochromatic subgraphs, each of which is isomorphic to an element of F, whose vertex sets partition V(Kn). This proves a conjecture of Corsten and Mendonça in a strong form and generalizes results on the multicolour Ramsey numbers of bounded-degree bipartite graphs.