Squarefree Powers of Edge Ideals of Forests

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