First, construct a tournament scheme: number the 18 teams sequentially as $1, 2, \cdots, 18$, and form two subsets according to odd and even numbers:
$$A=\{1,3, \cdots, 17\}, B=\{2,4, \cdots, 18\},$$

Then, the teams $(x, y)$ for each match are assigned to rounds based on the remainder when $x+y$ is divided by 9. First, arrange 4 matches between teams of the same parity, then arrange one match for the "odd team out," requiring that in the $r$-th round, each match's teams $(x, y)$ satisfy:
$$x+y \equiv r(\bmod 9) .$$