Regularity of Edge Ideals and Their Powers

By Arindam Banerjee, Selvi Kara, Huy Tài Hà. Advances in Algebra, 2017

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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 $G.$

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/4d04acde78b954223fb40c021f723191d124734b