Unmixed and Cohen--Macaulay weighted oriented König graphs

Yuriko Pitones, Enrique Reyes, Rafael H. Villarreal

Let $D$ be a weighted oriented graph, whose underlying graph is $G$, and let $I(D)$ be its edge ideal. If $G$ has no $3$-, $5$-, or $7$-cycles, or $G$ is König, we characterize whe…