The minimum-fort-size conjecture for marginal observances

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Let GG be a graph. Write f‾(G)\underline{f}(G) for the minimum fort size of GG, let MObs(G;i)\mathrm{MObs}(G;i) denote the marginal observance at step ii, and let γP(G)\gamma_P(G) denote the power domination number. For a positive integer kk, write [k]={1,…,k}[k]=\{1,\ldots,k\}. Minimum-fort-size conjecture. If

f‾(G)≥4,\underline{f}(G)\geq 4,

then

MObs(G;i)≥4\mathrm{MObs}(G;i)\geq 4

for all i∈[γP(G)]i\in[\gamma_P(G)]. This asks whether the relationship between minimum fort size and marginal observances established for smaller minimum fort sizes extends to minimum fort size at least four; its status is not resolved in the source.

References

Primary source

Beth Bjorkman, Sean English and Johnathan Koch, “Cost-Benefit Analysis for PMU Placement in Power Grids”, arXiv:2601.19775 (2026).

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