2 problems

Let $G$ be a chordal graph, let $I(G)$ be its edge ideal, let $I(G)^{[k]}$ denote its $k$-th square-free power, let $\nu(G)$ be its matching number, and let $\mathrm{aim}(G,k)$ be…

Let $G$ be a forest, let $I(G)$ be its edge ideal, let $I(G)^{[k]}$ denote its $k$-th square-free power, let $\nu(G)$ be its matching number, and let $\mathrm{aim}(G,k)$ be the max…