  Let $I$ be the edge ideal of a Cohen-Macaulay tree of dimension $d$ over a
polynomial ring $S = \mathrm{k}[x_1,\ldots,x_{d},y_1,\ldots,y_d]$. We prove
that for all $t \ge 1$,
  $$\operatorname{depth} (S/I^t) = \operatorname{max} \{d -t + 1, 1 \}.$$

Commutative Algebra;Combinatorics