Well-failed graphs
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866913673262399488 |
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| author | Jacob, Bonnie |
| author_facet | Jacob, Bonnie |
| contents | In this paper we begin the study of well-failed graphs, that is, graphs in which every maximal failed zero forcing set is a maximum failed zero forcing set, or equivalently, in which every minimal fort is a minimum fort. We characterize trees that are well-failed. Along the way, we prove that the set of vertices in a graph that are not in any minimal fort is identical to the set of vertices that are in no minimal zero forcing set, which allows us to characterize vertices in a tree that are in no minimal fort. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_19357 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Well-failed graphs Jacob, Bonnie Combinatorics 05C50 In this paper we begin the study of well-failed graphs, that is, graphs in which every maximal failed zero forcing set is a maximum failed zero forcing set, or equivalently, in which every minimal fort is a minimum fort. We characterize trees that are well-failed. Along the way, we prove that the set of vertices in a graph that are not in any minimal fort is identical to the set of vertices that are in no minimal zero forcing set, which allows us to characterize vertices in a tree that are in no minimal fort. |
| title | Well-failed graphs |
| topic | Combinatorics 05C50 |
| url | https://arxiv.org/abs/2501.19357 |