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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