2021/03/10 by Xun Chen, Chen, Xun, Qizhong Lin +3
Computer Science · Mathematics · #05D10 #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.2103.05814
openalex publication_date 2021/03/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A book Bn is a graph which consists of n triangles sharing a common edge. In 1978, Rousseau and Sheehan conjectured that the Ramsey number satisfies r(Bm,Bn)≤ 2(m+n)+c for some constant c>0. In this paper, we obtain that r(Bm, Bn)≤ 2(m+n)+o(n) for all m≤ n and n large, which confirms the conjecture of Rousseau and Sheehan asymptotically. As a corollary, our result implies that a related conjecture of Faudree, Rousseau and Sheehan (1982) on strongly regular graph holds asymptotically.