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

Regularity of Edge Ideals and Their Powers

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classification math.AC math.CO
keywords edgeidealspowersregularitytextasymptoticboundscastelnuovo-mumford
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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 $G.$

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