2022/02/26 by Yaser Rowshan, Rowshan, Yaser
Computer Science · Engineering · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Limits and Structures in Graph Theory #graph theory and CDMA systems #math.CO
paper · pdf · doi:10.48550/arxiv.2202.13167
arXiv admin note: substantial text overlap with arXiv:2202.09645
arxiv created 2022/02/26 · openalex publication_date 2022/02/26 · arxiv updated 2022/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given bipartite graphs G1, …, Gn, the bipartite Ramsey number BR(G1,…, Gn) is the last integer b such that any complete bipartite graph Kb,b with edges coloured with colours 1,2,…,n contains a copy of some Gi (1≤ i≤ n) where all edges of Gi have colour i. As another view of bipartite Ramsey numbers, for given bipartite graphs G1, …, Gn and a positive integer m, the m-bipartite Ramsey number BRm(G1, …, Gn), is defined as the least integer b, such that any complete bipartite graph Km,b with edges coloured with colours 1,2,…,n contains a copy of some Gi (1≤ i≤ n) where all edges of Gi have colour i. The size of BRm(G1, G2), where G1=K2,2 and G2∈ \K3,3, K4,4\ for each m and the size of BRm(K3,3, K3,3) and BRm(K2,2, K5,5) for special values of m, have been determined in several article up to now. In this article, we compute the size of BRm(K2,2, K6,6) for some m≥ 2.