  In analogy to the skeletons of a simplicial complex and their
Stanley--Reisner ideals we introduce the skeletons of an arbitrary monomial
ideal $I\subset S=K[x_1,...,x_n]$. This allows us to compute the depth of $S/I$
in terms of its skeleton ideals. We apply these techniques to show that
Stanley's conjecture on Stanley decompositions of $S/I$ holds provided it holds
whenever $S/I$ is Cohen--Macaulay. We also discuss a conjecture of
Soleyman-Jahan and show that it suffices to prove his conjecture for monomial
ideals with linear resolution.
