Regularity of Path Ideals of Gap Free Graphs
Arindam Banerjee
TL;DR
This paper investigates the Castelnuovo-Mumford regularity of path ideals in finite simple graphs, providing new bounds and showing linear resolutions for specific classes like gap free and claw graphs.
Contribution
It introduces new upper bounds for the regularity of path ideals in gap free graphs and proves linear resolutions for certain graph classes.
Findings
New upper bounds for path ideal regularity
Linear minimal free resolutions for gap free and claw graphs
Enhanced understanding of algebraic properties of graph ideals
Abstract
In this paper we study the Castelnuovo-Mumford regularity of the path ideals of finite simple graphs. We find new upper bounds for various path ideals of gap free graphs. In particular we prove that the path ideals of gap free and claw graphs have linear minimal free resolutions.
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