Path Ideals of Weighted Graphs

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 $r=2$).

24 pages

References in corpus (1)

• Edge Ideals of Weighted Graphs