On robust toric ideals of weighted oriented graphs

Ramakrishna Nanduri; Tapas Kumar Roy

paper

On robust toric ideals of weighted oriented graphs

arXiv:2504.15200

Abstract

In this work, we study the equivalence of various robustness properties of toric ideals of weighted oriented graphs. For any weighted oriented graph $D$ , if its toric ideal $I_{D}$ is generalized robust (or weakly robust), then we show that $D$ does not have forbidden subgraphs $D_{1}, D_{2}$ of certain structures. We give a significant class of weighted oriented graphs $D$ whose toric ideals $I_{D}$ have the following equivalence. (i) $I_{D}$ is strongly robust (equivalently, $I_{D}$ is robust); (ii) $I_{D}$ is generalized robust (equivalently, $I_{D}$ is weakly robust); (iii) $D$ does not have subgraphs equal to $D_{1}$ and $D_{2}$ .

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