Ramsey numbers of connected 4-clique matching

06/14/2023

∙

by   Krit Kanopthamakun, et al.

∙

0

∙

share

We determine the exact value of the 2-color Ramsey number of a connected 4-clique matching 𝒞(nK_4) which is a set of connected graphs containing n disjoint K_4. That is, we show that R_2(𝒞(nK_4)) = 13n-3 for any positive integer n ≥ 3. The result is an extension of the result by (Roberts, 2017) which gave that result when n≥ 18. We also show that the result still holds when n=2 provided that R_2(2K_4) ≤ 23.