DEPTH AND STANLEY DEPTH OF POWERS OF THE EDGE IDEALS OF SOME CATERPILLAR AND LOBSTER TREES.

Let S be a ring of polynomials in finitely many variables over a field. In this paper, we give lower bounds for depth and Stanley depth of modules of the type S/I^t for t = 1, where I is the edge ideal of some caterpillar and lobster trees. These new bounds are much sharper than the existing bounds for the classes of ideals we considered. [ABSTRACT FROM AUTHOR]