Structural properties of admissible subgraphs and the depth of symbolic powers of cover ideals

Nguyen Thu Hang, Nguyen Thi Thanh Tam, Thanh Vu

Let $G$ be a simple graph with cover ideal $J(G)$ in a polynomial ring $S = \k[x_1, \ldots, x_n]$. For each integer $t\ge 1$, let ${\alpha }_t(G)$ denote the maximum size of an ordered ma…