Matchings and squarefree powers of edge ideals
Nursel Erey, J\"urgen Herzog, Takayuki Hibi, Sara Saeedi Madani
TL;DR
This paper investigates the algebraic properties of squarefree powers of edge ideals, focusing on regularity bounds, linear resolutions, and the squarefree Ratliff property, all in relation to graph matchings.
Contribution
It provides new bounds for the regularity of squarefree powers and explores conditions for linear resolutions and the squarefree Ratliff property in edge ideals.
Findings
Established bounds for regularity of squarefree powers.
Identified conditions for linear relations and resolutions.
Analyzed the squarefree Ratliff property in this context.
Abstract
Squarefree powers of edge ideals are intimately related to matchings of the underlying graph. In this paper we give bounds for the regularity of squarefree powers of edge ideals, and we consider the question of when such powers are linearly related or have linear resolution. We also consider the so-called squarefree Ratliff property.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Rings, Modules, and Algebras