Squarefree powers of edge ideals of forests

Abstract

Let I(G)([k]) denote the kth squarefree power of the edge ideal of G. When G is a forest, we provide a sharp upper bound for the regularity of I(G)([k]) in terms of the k-admissable matching number of G. For any positive integer k, we classify all forests G such that I(G)([k]) has linear resolution. We also give a combinatorial formula for the regularity of I(G)([2]) for any forest G.