Cameron's fort-number lower-bound conjecture for maximum nullity

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Let GG be a graph, let ft⁡(G)\operatorname{ft}(G) be its fort number, let Z⁡∗(G)\operatorname{Z}^*(G) be its fractional zero forcing number, and let M⁡(G)\operatorname{M}(G) be its maximum nullity.

Cameron's conjecture. For every graph GG,

ft⁡(G)≤Z⁡∗(G)≤M⁡(G).\operatorname{ft}(G)\leq \operatorname{Z}^*(G)\leq \operatorname{M}(G).

The first inequality is the known general fort-number bound for fractional zero forcing. The conjecture asserts the additional lower bound on maximum nullity; it is motivated by the established inequality M⁡(G)≤Z⁡(G)\operatorname{M}(G)\leq \operatorname{Z}(G) and the need for lower bounds on maximum nullity.

References

Primary source

Thomas R. Cameron and Jonad Pulaj, “IP Models for Minimum Zero Forcing Sets, Forts, and Related Graph Parameters”, arXiv:2508.07293 (2025).

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