Regularity of Edge Ideals and Their Powers

Published 4 Dec 2017 in math.AC and math.CO | (1712.00887v2)

Abstract: We survey recent studies on the Castelnuovo-Mumford regularity of edge ideals of graphs and their powers. Our focus is on bounds and exact values of $\text{reg} I(G)$ and the asymptotic linear function $\text{reg} I(G)^q$, for $q \geq 1,$ in terms of combinatorial data of the given graph $G.$

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