Time: 9h00, Wednesday, October 15, 2014

Location: Room 6, Building A14, Institute of Mathematics, 18 Hoang Quoc Viet, Cau Giay, Hanoi

Abstract: Let $G$ be a graph and let $I = I(G)$ be its edge ideal. In this paper, when $G$ is a forest or a cycle, we explicitly compute the regularity of $I^s$ for all $s geqslant  1$. In particular, for this class of graphs, we provide the asymptotic linear function $reg(I^s)$ as $s gg 0$, and the initial value of $s$ starting from which $reg(I^s)$ attains its linear form. We also give new bounds on the regularity of $I$ when $G$ contains a Hamiltonian path and when $G$ is a Hamiltonian graph. (This is a joint work with Salvi Bayarslam and Ha Huy Tai)