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- W4322588894 abstract "Let $G$, $H$ and $K$ represent three graphs without loops or parallel edges and $n$ represent an integer. Given any red blue coloring of the edges of $G$, we say that $K rightarrow (G,H)$, if there exists red copy of $G$ in $K$ or a blue copy of $H$ in $K$. Let $K_n$ represent a complete graph on $n$ vertices, $C_n$ a cycle on $n$ vertices and $S_n=K_{1,n}$ a star on $n+1$ vertices. The Ramsey number $r(G, H)$ is defined as $min{n mid K_nrightarrow (G,H)}$. Likewise, the star-critical Ramsey number $r_*(H, G)$ is defined $min{k mid K_{r(G,H)-1} sqcup K_{1,k} rightarrow (H, G) }$. When $n >3$, in this paper we show that $r_*(C_n,K_5)=3n-1$ except $r_*(C_4,K_5)=13$. We also characterize all Ramsey critical $r(C_n,K_5)$ graphs." @default.
- W4322588894 created "2023-02-28" @default.
- W4322588894 creator A5046189561 @default.
- W4322588894 date "2019-01-15" @default.
- W4322588894 modified "2023-09-27" @default.
- W4322588894 title "Star-critical Ramsey numbers for cycles versus the complete graph on 5 vertices" @default.
- W4322588894 doi "https://doi.org/10.48550/arxiv.1901.04802" @default.
- W4322588894 hasPublicationYear "2019" @default.
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