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arXiv · 2609.11754

Fort Abundance in Zero Forcing

Aida Abiad·Sina Ghasemi Nezhad
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Abstract

This paper paper concerns the study of forts, the sets that obstruct zero forcing. We show that every block graph on $n$ vertices has at least $n/3$ minimal forts, extending a recent bound for trees by Cameron and and Li (arXiv:2512.12874). The number of forts, and with it the number of compatible collections, grows exponentially for every tree, every connected non-star graph of bounded degree, and every connected graph of linear minimum degree, answering a question in the negative by Hicks et al. (INFORMS Journal on Computing 2022) for these graph classes. We finish by counting the minimal forts of a tree exactly, in linear time and space.

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Aida Abiad, Sina Ghasemi Nezhad. 2026-09-10. Fort Abundance in Zero Forcing. https://arxiv.org/abs/2609.11754

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