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arXiv · 2501.19357

Well-failed graphs

Bonnie Jacob
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Abstract

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.

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Bonnie Jacob. 2025-01-31. Well-failed graphs. https://arxiv.org/abs/2501.19357

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