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Regularity of Edge Ideals and Their Powers

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arxiv 1712.00887 v2 pith:YOHYL4MB submitted 2017-12-04 math.AC math.CO

Arindam Banerjee , Selvi Kara , Huy Tai Ha This is my paper · ORCID
classification math.ACmath.CO
keywords edgeidealspowersregularitytextasymptoticboundscastelnuovo-mumford
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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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