Algebra Seminar - A.V. Jayanthan - Upper bounds for the regularity of powers of edge ideals of graphs
Speaker: A.V. Jayanthan (Indian Institute of TechnologyMadras)
Title: Upper bounds for the regularity of powers of edge ideals of graphs.
Abstract: Let $G$ be a finite simple graph and $I(G)$ denote the corresponding edge ideal. In this talk, we will discuss about upper bounds for the Castelnuovo-Mumford regularity of $I(G)^q$ in terms of certain combinatorial invariants associated with $G$. We also prove a weaker version of a conjecture by Alilooee, Banerjee, Beyarslan and Ha on an upper bound for the regularity of $I(G)^q$ and we prove the conjectured upper bound for the class of vertex decomposable graphs. Using these results, we explicitly compute the regularity of $I(G)^q$ for several classes of graphs. This is a joint work with S. Selvaraja.