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2017•arXiv (Cornell University)Open access

Linear polynomial for the regularity of powers of edge ideals of very well-covered graphs

A. V. Jayanthan, S. Selvaraja

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Abstract

Let $G$ be a finite simple graph and $I(G)$ denote the corresponding edge ideal. In this paper we prove that if $G$ is a very well-covered graph then for all $s \geq 2$ the regularity of $I(G)^s$ is exactly $2s+ν(G)-1$.

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Let $G$ be a finite simple graph and $I(G)$ denote the corresponding edge ideal. In this paper we prove that if $G$ is a very well-covered graph then for all $s \geq 2$ the regularity of $I(G)^s$ is exactly $2s+ν(G)-1$.

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Available abstract

Let $G$ be a finite simple graph and $I(G)$ denote the corresponding edge ideal. In this paper we prove that if $G$ is a very well-covered graph then for all $s \geq 2$ the regularity of $I(G)^s$ is exactly $2s+ν(G)-1$.

Key concepts: Enhanced Data Rates for GSM Evolution, Mathematics, Polynomial, Pure mathematics, Mathematical economics, Combinatorics, Computer science, Mathematical analysis

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