Salvato in:
| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2504.15200 |
| Tags: |
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Sommario:
- 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 $D_{2}$.