Geodesic
Ramsey numbers of fans and large books
The electronic journal of combinatorics, Tome 29 (2022) no. 1
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For graphs $G$ and $H$, the Ramsey number $R(G,H)$ is the minimum integer $N$ such that any red/blue edge coloring of $K_N$ contains either a red $G$ or a blue $H$. Let $G+H$ be the graph obtained from vertex disjoint $G$ and $H$ by adding new edges connecting $G$ and $H$ completely, $F_m=K_1+mK_2$ and $B_p(n)=K_p+nK_1$. It is shown $R(F_m,B_p(n))=2(n+p-1)+1$ for fixed $m, p$ and large $n$.
DOI : 10.37236/10742
Classification : 05C55, 05D10 
@article{10_37236_10742,
     author = {Meng Liu and Yusheng Li},
     title = {Ramsey numbers of fans and large books},
     journal = {The electronic journal of combinatorics},
     year = {2022},
     volume = {29},
     number = {1},
     doi = {10.37236/10742},
     zbl = {1486.05196},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/10742/}
}
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Meng Liu; Yusheng Li. Ramsey numbers of fans and large books. The electronic journal of combinatorics, Tome 29 (2022) no. 1. doi: 10.37236/10742

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