The (d−2)(d-2)-leaky forcing number conjecture for hypercubes

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Let QdQ_d be the dd-dimensional hypercube, and let Z(d−2)(Qd)Z_{(d-2)}(Q_d) denote its (d−2)(d-2)-leaky forcing number.

Hypercube leaky forcing conjecture.

Z(d−2)(Qd)=2d−1.Z_{(d-2)}(Q_d)=2^{d-1}.

The paper establishes an upper bound for this quantity, but the matching lower bound is not known; partial results for hypercubes motivate the conjectured equality.

References

Primary source

Rebekah Herrman, “Upper bound for the (d-2)-leaky forcing number of Q_d and -leaky forcing number of GP(n,1)”, arXiv:2202.12671 (2022).

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