2019/02/05 by Chula J. Jayawardene, Jayawardene, Chula J., W. C. W. Navaratna +3
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.1902.02646
openalex publication_date 2019/02/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G and H be finite graphs. If for any two-coloring of the edges of a complete graph Kn, there is a copy of G in the first color, red, or a copy of H in the second color, blue, we will say Kn→ (G,H). The Ramsey number r(G, H) is defined as the smallest positive integer n such that Kn → (G, H). A two-coloring of Kr(G, H)-1 such that Kr(G, H)-1 \not → (G,H) is called a critical coloring. A Ramsey critical r(G, H) graph is a graph induced by the first color of a critical coloring. In this paper, when n ≥ 15, we show that there exist exactly sixty eight non-isomorphic Ramsey critical r(Cn, K6) graphs.