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arXiv · 2204.10317

The $v$-number and Castelnuovo-Mumford regularity of graphs

Yusuf Civan
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Abstract

We prove that for every integer $k\geq 1$, there exists a connected graph $H_k$ such that $v(H_k)=reg(H_k)+k$, where $v(G)$ and $reg(G)$ denote the $v$-number and the (Castelnuovo-Mumford) regularity of a graph $G$ respectively.

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Yusuf Civan. 2022-04-21. The $v$-number and Castelnuovo-Mumford regularity of graphs. https://arxiv.org/abs/2204.10317

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