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- W4308792757 abstract "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 $$r(K_{m},F_{t,n})=tn(m-1)+1$$ for $$mge 3$$ and sufficiently large n, where $$F_{t,n}=K_{1}+nK_{t}$$ . Recently, Hao and Lin proved that $$r(K_{3},F_{3,n})=6n+1$$ for $$nge 3$$ and $$r_{*}(K_{3},F_{3,n})=3n+3$$ for $$nge 4$$ . In this paper, we show that $$r(K_{m}, sF_{t,n})=tn(m+s-2)+s$$ for sufficiently large n and, in particular, $$r(K_{3}, sF_{t,n})=tn(s+1)+s$$ for $$tin {3,4},nge t$$ and $$sge 1$$ . We also show that $$r_{*}(K_{3}, F_{4,n})=4n+4$$ for $$nge 4$$ and establish an upper bound for $$r(F_{2,m},F_{t,n})$$ ." @default.
- W4308792757 created "2022-11-15" @default.
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- W4308792757 date "2022-11-11" @default.
- W4308792757 modified "2023-10-17" @default.
- W4308792757 title "Ramsey Numbers for Complete Graphs Versus Generalized Fans" @default.
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- W4308792757 doi "https://doi.org/10.1007/s00373-022-02590-z" @default.
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