Wu–Magnant–Nowbandegani–Xia conjecture for multicolor Ramsey numbers of cherries

Let $k,n_1,\ldots,n_k$ be positive integers, and let $n=\max\{n_1,\ldots,n_k\}$. Here $P_3$ is the path on three vertices, also called a cherry, and $R(n_1P_3,\ldots,n_kP_3)$ denotes the $k$-color Ramsey number for vertex-disjoint unions of the indicated numbers of cherries.

Wu–Magnant–Nowbandegani–Xia conjecture.

$$R(n_1P_3,\ldots,n_kP_3)=2n+\sum_{i=1}^{k}n_i-k+1.$$

The formula is known to be a general lower bound, arising from the standard construction for multicolor matching Ramsey numbers. The conjecture asserts that this lower bound is always tight; the general multicolor case remains open.