2019/07/11 by Tom Bohman, Bohman, Tom, Emily Zhu +1
Computer Science · Mathematics · #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.1907.05236
openalex publication_date 2019/07/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let H be a 3-uniform hypergraph. The multicolor Ramsey number rk(H) is the smallest integer n such that every coloring of \binom[n]3 with k colors has a monochromatic copy of H. Let L be the loose 3-uniform path with 3 edges and M denote the messy 3-uniform path with 3 edges; that is, let L = \abc, cde, efg\ and M = \ abc, bcd, def\. In this note we prove rk(L) < 1.54k and rk(M) < 1.6k for k sufficiently large.