2015/06/15 by Arie Bialostocki, Bialostocki, Arie, András Gyárfás +2 · 1 citation
Computer Science · Mathematics · #Advanced Graph Theory Research #Advanced Topology and Set Theory #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #math.CO
paper · pdf · doi:10.48550/arxiv.1506.04495
arxiv created 2015/06/15 · openalex publication_date 2015/06/15 · arxiv updated 2015/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We extend two well-known results in Ramsey theory from from Kn to arbitrary n-chromatic graphs. The first is a note of Erd\H os and Rado stating that in every 2-coloring of the edges of Kn there is a monochromatic tree on n vertices. The second is the theorem of Cockayne and Lorimer stating that for positive integers satisfying n1=max\n1,n2,…,nt\ and with n=n1+1+∑i=1t (ni-1), the following holds. In every coloring of the edges of Kn with colors 1,2…,t there is a monochromatic matching of size ni for some i∈ \1,2,…,t\.