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arXiv · 1609.01402

Regularity of Powers of Bipartite Graphs

A V Jayanthan·N Narayanan·S Selvaraja
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Abstract

Let $G$ be a finite simple graph and $I(G)$ denote the corresponding edge ideal. For all $s \geq 1$, we obtain upper bounds for reg$(I(G)^s)$ for bipartite graphs. We then compare the properties of $G$ and $G'$, where $G'$ is the graph associated with the polarization of the ideal $(I(G)^{s+1} : e_1\cdots e_s)$, where $e_1,\ldots e_s$ are edges of $G$. Using these results, we explicitly compute reg$(I(G)^s)$ for several subclasses of bipartite graphs.

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A V Jayanthan, N Narayanan, S Selvaraja. 2016-09-06. Regularity of Powers of Bipartite Graphs. https://arxiv.org/abs/1609.01402

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