2021/11/11 by Maoqun Wang, Wang, Maoqun, Jianguo Qian +1 · 1 citation
Computer Science · Mathematics · #05C55 #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.2111.06107
openalex publication_date 2021/11/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For two graphs G and H, let r(G,H) and r_*(G,H) denote the Ramsey number and star-critical Ramsey number of G versus H, respectively. In 1996, Li and Rousseau proved that r(Km,Ft,n)=tn(m-1)+1 for m≥ 3 and sufficiently large n, where Ft,n=K1+nKt. Recently, Hao and Lin proved that r(K3,F3,n)=6n+1 for n≥ 3 and r∗(K3,F3,n)=3n+3 for n≥ 4. In this paper, we show that r(Km, sFt,n)=tn(m+s-2)+s for sufficiently large n and, in particular, r(K3, sFt,n)=tn(s+1)+s for t∈\3,4\,n≥ t and s≥1. We also show that r∗(K3, F4,n)=4n+4 for n≥ 4 and establish an upper bound on r(F2,m,Ft,n).