Path ideals of weighted graphs

Bethany Kubik; Sean Sather-Wagstaff

doi:10.1016/j.jpaa.2014.12.027

Path ideals of weighted graphs

Bethany Kubik, Sean Sather-Wagstaff

Mathematics & Statistics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We introduce and study the weighted r-path ideal of a weighted graph G_ω, which is a common generalization of Conca and De Negri's r-path ideal for unweighted graphs and Paulsen and Sather-Wagstaff's edge ideal of the weighted graph. Over a field, we explicitly describe primary decompositions of these ideals, and we characterize Cohen-Macaulayness of these ideals for trees (with arbitrary r) and complete graphs (for r=2).

Original language	English (US)
Pages (from-to)	3889-3912
Number of pages	24
Journal	Journal of Pure and Applied Algebra
Volume	219
Issue number	9
DOIs	https://doi.org/10.1016/j.jpaa.2014.12.027
State	Published - Sep 1 2015

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abstract = "We introduce and study the weighted r-path ideal of a weighted graph Gω, which is a common generalization of Conca and De Negri's r-path ideal for unweighted graphs and Paulsen and Sather-Wagstaff's edge ideal of the weighted graph. Over a field, we explicitly describe primary decompositions of these ideals, and we characterize Cohen-Macaulayness of these ideals for trees (with arbitrary r) and complete graphs (for r=2).",

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AB - We introduce and study the weighted r-path ideal of a weighted graph Gω, which is a common generalization of Conca and De Negri's r-path ideal for unweighted graphs and Paulsen and Sather-Wagstaff's edge ideal of the weighted graph. Over a field, we explicitly describe primary decompositions of these ideals, and we characterize Cohen-Macaulayness of these ideals for trees (with arbitrary r) and complete graphs (for r=2).

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