Ramsey numbers of large even cycles and fans
The electronic journal of combinatorics, Tome 30 (2023) no. 3
For graphs $F$ and $H$, the Ramsey number $R(F, H)$ is the smallest positive integer $N$ such that any red/blue edge coloring of $K_N$ contains either a red $F$ or a blue $H$. Let $C_n$ be a cycle of length $n$ and $F_n$ be a fan consisting of $n$ triangles all sharing a common vertex.In this paper, we prove that for all sufficiently large $n$,\[R(C_{2\lfloor an\rfloor}, F_n)= \left\{ \begin{array}{ll}(2+2a+o(1))n & \textrm{if $1/2\leq a< 1$,}\\(4a+o(1))n & \textrm{if $ a\geq 1$.}\end{array} \right.\]
@article{10_37236_11068,
author = {Chunlin You and Qizhong Lin},
title = {Ramsey numbers of large even cycles and fans},
journal = {The electronic journal of combinatorics},
year = {2023},
volume = {30},
number = {3},
doi = {10.37236/11068},
zbl = {1535.05260},
url = {http://geodesic.mathdoc.fr/articles/10.37236/11068/}
}
Chunlin You; Qizhong Lin. Ramsey numbers of large even cycles and fans. The electronic journal of combinatorics, Tome 30 (2023) no. 3. doi: 10.37236/11068
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