Let $\Delta$ be a simplicial complex on vertex set $ [n]$. It is shown that if $\Dlta$ is complete intersection, Cohen–Macaulay of codimension 2, Gorenstein of codimension 3, or 2-Cohen–Macaulay of codimension 3, then $\Delta$ is vertex decomposable. As a consequence, we show that if $\Dlta$ is a simplicial complex such that $ I_{Delta} = I_t (C_n)$, where I_t (C_n)$ is the path ideal of length $t$ of $C_n$, then $\Delta$ is vertex decomposable if and only$ if $t = n, t = n − 1$, or $n $ is odd and $ t = (n − 1)/2$
