2023/09/13 by Joseph Hyde, Hyde, Joseph, Jae-baek Lee +3 · 1 citation
Computer Science · Mathematics · #05C35 #05D10 #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.2309.06959
openalex publication_date 2023/09/13 · openalex created_date 2023/09/15 · openalex updated_date 2026/08/01
The Ramsey multiplicity constant of a graph H is the limit as n tends to infinity of the minimum density of monochromatic labeled copies of H in a 2-edge colouring of Kn. Fox and Wigderson recently identified a large family of graphs whose Ramsey multiplicity constants are attained by sequences of ``Turán colourings''; i.e. colourings in which one of the colour classes forms the edge set of a balanced complete multipartite graph. Each graph in their family comes from taking a connected non-3-colourable graph with a critical edge and adding many pendant edges. We extend their result to an off-diagonal variant of the Ramsey multiplicity constant which involves minimizing a weighted sum of red copies of one graph and blue copies of another.