Year: 2026
Type: preprint
Abstract: A graph $H$ is called common if the number of monochromatic copies of $H$ in a $2$-edge-coloring of a large complete graph is asymptotically minimized by the random coloring with an equal proportion of each color. The house graph and $K_4$ with one edge subdivided once are known to be common by the flag algebra method. Grzesik, Lee, Lidický, and Volec asked for ``human-friendly'' proofs of the commonality of these two graphs. In this short note, we give flag-algebra-free proofs that both graphs are common.
Source: arXiv (Cornell University)
Author: Chen, Hao
Institution: Soochow University
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221852027