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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 ofthe 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 S\'ark\"ozy and laterimprovement by Davies, Jenssen and Roberts give an upper bound of $(k -\frac{1}{4} + o(1))n$. We improve the upper bound to $(k - \frac{1}{2}+o(1))n$. Our approach uses structural insights in connected graphs without alarge matching. These insights may be of independent interest.

Improved bounds on the multicolor Ramsey numbers of paths and even cycles