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arXiv · 1810.07140

Regularity and $h$-polynomials of edge ideals

Takayuki Hibi·Kazunori Matsuda·Adam Van Tuyl
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Abstract

For any two integers $d,r \geq 1$, we show that there exists an edge ideal $I(G)$ such that the ${\rm reg}\left(R/I(G)\right)$, the Castelnuovo-Mumford regularity of $R/I(G)$, is $r$, and ${\rm deg} (h_{R/I(G)}(t))$, the degree of the $h$-polynomial of $R/I(G)$, is $d$. Additionally, if $G$ is a graph on $n$ vertices, we show that ${\rm reg}\left(R/I(G)\right) + {\rm deg} (h_{R/I(G)}(t)) \leq n$.

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Takayuki Hibi, Kazunori Matsuda, Adam Van Tuyl. 2018-10-16. Regularity and $h$-polynomials of edge ideals. https://arxiv.org/abs/1810.07140

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