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arXiv · 1905.02141

Matching numbers and the regularity of the Rees algebra of an edge ideal

Jürgen Herzog·Takayuki Hibi
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Abstract

The regularity of the Rees ring of the edge ideal of a finite simple graph is studied. We show that the matching number is a lower and matching number~$+1$ is an upper bound of the regularity, if the Rees algebra is normal. In general the induced matching number is a lower bound for the regularity, which can be shown by applying the squarefree divisor complex.

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Jürgen Herzog, Takayuki Hibi. 2019-05-06. Matching numbers and the regularity of the Rees algebra of an edge ideal. https://arxiv.org/abs/1905.02141

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