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

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.

Sources & referencesView supporting material

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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