Lower bound on the size-Ramsey number of tight paths

The size-Ramsey number $R^{(k)}(H)$ of a $k$-uniform hypergraph $H$ is the minimum edges in $G$ with property that each $2$-edge coloring contains monochromatic copy $H$. For $k\ge2$ and $n\in\mathbb{N}$, tight path on $n$ vertices $P^{(k)}_{n,k-1}$ defined as for which there an ordering its such edge set consists all $k$-element intervals consecutive this ordering. We show lower bound paths, is, considered assymptotically both uniformity $k$ $n$, $R^{(k)}(P^{(k)}_{n,k-1})= \Omega_{n,k}\big(\log (k)n\big)$.