Regularity of edge ideals and their powers

Official URL: https://risc01.sabanciuniv.edu/record=b2553644 _(Table of contents)

In this thesis, we study the Castelnuovo-Mumford regularity of edge ideals associated to graphs. We rst give a detailed proof of celebrated theorem of Fr7Foberg which characterizes edge ideals with linear resolution. We also collect recent results on di erent bounds and exact values of regularity of edge ideals associated to different classes of graphs. In the last part, we study some bounds and exact values of regularity of powers of edge ideals.