Solution
= Solution
Colour the vertices of $K_{(s-1)t}$ in $s-1$ groups of size $t$. Colour edges within groups blue and edges between groups red. The red graph is complete $(s-1)$-partite, so it has no red $K_s$. Every blue component has only $t$ vertices, so it has no <path in a graph>[path] of length $t$. Therefore
$$
\boxed{r(K_s,P_t)\geq(s-1)t+1.}
$$