%0 Journal Article
%T Path Ideals of Weighted Graphs
%A Bethany Kubik
%A Sean Sather-Wagstaff
%J Mathematics
%D 2014
%I arXiv
%X 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 $r=2$).
%U http://arxiv.org/abs/1408.1674v1