stanley's conjecture on the k-cohen-macaulay simplicial complexes of codimension 3

Let $delta$ be a simplicial complex on vertex set $[n]$. ##it is shown that if $delta$ is k-cohen--macaulay of codimension 3, then $delta$ is vertex decomposable.## as a consequence we show that $delta$ is partitionable and stanley s conjecture holds for $k[delta]$.