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 $K_n$. 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.
@article{10_37236_12751,
author = {Joseph Hyde and Jae-baek Lee and Jonathan A. Noel},
title = {Tur\'an colourings in off-diagonal {Ramsey} multiplicity},
journal = {The electronic journal of combinatorics},
year = {2025},
volume = {32},
number = {2},
doi = {10.37236/12751},
zbl = {1564.05103},
url = {http://geodesic.mathdoc.fr/articles/10.37236/12751/}
}
TY - JOUR
AU - Joseph Hyde
AU - Jae-baek Lee
AU - Jonathan A. Noel
TI - Turán colourings in off-diagonal Ramsey multiplicity
JO - The electronic journal of combinatorics
PY - 2025
VL - 32
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/12751/
DO - 10.37236/12751
ID - 10_37236_12751
ER -
%0 Journal Article
%A Joseph Hyde
%A Jae-baek Lee
%A Jonathan A. Noel
%T Turán colourings in off-diagonal Ramsey multiplicity
%J The electronic journal of combinatorics
%D 2025
%V 32
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/12751/
%R 10.37236/12751
%F 10_37236_12751
Joseph Hyde; Jae-baek Lee; Jonathan A. Noel. Turán colourings in off-diagonal Ramsey multiplicity. The electronic journal of combinatorics, Tome 32 (2025) no. 2. doi: 10.37236/12751
