2023/09/15 by Xueliang Li, Li, Xueliang, Yuan Si +1 · 1 citation
Computer Science · Mathematics · #05C15 05C30 05C55 #Advanced Graph Theory Research #Advanced Topology and Set Theory #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory
paper · pdf · doi:10.48550/arxiv.2309.08370
openalex publication_date 2023/09/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G, H be two non-empty graphs and k be a positive integer. The Gallai-Ramsey number grk(G:H) is defined as the minimum positive integer N such that for all n≥ N, every k-edge-coloring of Kn contains either a rainbow subgraph G or a monochromatic subgraph H. The Gallai-Ramsey multiplicity GMk(G:H) is defined as the minimum total number of rainbow subgraphs G and monochromatic subgraphs H for all k-edge-colored Kgrk(G:H). In this paper, we get some exact values of the Gallai-Ramsey multiplicity for rainbow small trees versus general monochromatic graphs under a sufficiently large number of colors. We also study the bipartite Gallai-Ramsey multiplicity.