Partite-set comparison conjecture for expected propagation times of complete bipartite graphs

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Let Km,nK_{m,n} have partite vertex sets RR and R′R' of orders mm and nn respectively, and let u∈Ru\in R and v∈R′v\in R'. Partite-set comparison conjecture. If n>3n>3 and m<nm<n, then

ept⁡(Km,n,{u})>ept⁡(Km,n,{v}).\operatorname{ept}(K_{m,n},\{u\})>\operatorname{ept}(K_{m,n},\{v\}).

The conjecture asserts that, except for the noted small outlier, starting from a vertex in the larger partite set gives a smaller expected propagation time. Its status is not established in the supplied material.

References

Primary source

Yu Chan, Emelie Curl, Jesse Geneson, Leslie Hogben, Kevin Liu, Issac Odegard and Michael S. Ross, “Using Markov chains to determine expected propagation time for probabilistic zero forcing”, arXiv:1906.11083 (2019).

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