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Upper bounds for the regularity of powers of edge ideals of graphs

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arxiv 1805.01412 v2 pith:2EC3HYMT submitted 2018-05-03 math.AC math.CO

A. V. Jayanthan , S. Selvaraja This is my paper · ORCID
classification math.ACmath.CO
keywords regularityuppergraphsboundboundsedgeprovealilooee
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abstract

Let $G$ be a finite simple graph and $I(G)$ denote the corresponding edge ideal. In this paper, we obtain upper bounds for the Castelnuovo-Mumford regularity of $I(G)^q$ in terms of certain combinatorial invariants associated with $G$. We also prove a weaker version of a conjecture by Alilooee, Banerjee, Beyarslan and H\`a on an upper bound for the regularity of $I(G)^q$ and we prove the conjectured upper bound for the class of vertex decomposable graphs. Using these results, we explicitly compute the regularity of $I(G)^q$ for several classes of graphs.

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  1. Regularity of Edge Ideals Via Suspension

    math.AC 2019-08 conditional novelty 7.0 of 10

    For every bipartite graph G and every s >= 2, the Castelnuovo-Mumford regularity of the s-th power of its edge ideal is at most 2s + reg(I(G)) - 2, and this bound is tight.

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