# Improved Bounds on the Multicolor Ramsey Numbers of Paths and Even Cycles

@article{Knierim2019ImprovedBO, title={Improved Bounds on the Multicolor Ramsey Numbers of Paths and Even Cycles}, author={Charlotte Knierim and Pascal Su}, journal={Electron. J. Comb.}, year={2019}, volume={26}, pages={P1.26} }

We study the multicolor Ramsey numbers for paths and even cycles, $R_k(P_n)$ and $R_k(C_n)$, which are the smallest integers $N$ such that every coloring of the complete graph $K_N$ has a monochromatic copy of $P_n$ or $C_n$ respectively. For a long time, $R_k(P_n)$ has only been known to lie between $(k-1+o(1))n$ and $(k + o(1))n$. A recent breakthrough by Sárközy and later improvement by Davies, Jenssen and Roberts give an upper bound of $(k - \frac{1}{4} + o(1))n$. We improve the upper bound… Expand

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