  Given a tree T on n vertices, there is an associated ideal I of a polynomial
ring in n variables over a field, generated by all paths of a fixed length of
T. We show that such an ideal always satisfies the Konig property and classify
all trees for which R/I is Cohen-Macaulay. More generally, we show that an
ideal I whose generators correspond to any collection of subtrees of T
satisfies the Konig property. Since the edge ideal of a simplicial tree has
this form, this generalizes a result of Faridi. Moreover, every square-free
monomial ideal can be represented (non-uniquely) as a subtree ideal of a graph,
so this construction provides a new combinatorial tool for studying square-free
monomial ideals. For a special class of trees, namely trees that are themselves
a path, a precise formula for the depth is given and it is shown that the proof
extends to provide a lower bound on the Stanley depth of these ideals.
Combining these results gives a new class of ideals for which the Stanley
Conjecture holds.
