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arXiv · 1408.1674

Path Ideals of Weighted Graphs

Bethany Kubik·Sean Sather-Wagstaff
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Abstract

We introduce and study the weighted $r$-path ideal of a weighted graph $G_\omega$, 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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Bethany Kubik, Sean Sather-Wagstaff. 2014-08-07. Path Ideals of Weighted Graphs. https://arxiv.org/abs/1408.1674

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