Zero forcing with random sets

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Bryan Curtis, Luyining Gan, Jamie Haddock, Rachel Lawrence, Sam Spiro

Published: 01 Jan 2024, Last Modified: 07 Oct 2025Discret. Math. 2024EveryoneRevisionsBibTeXCC BY-SA 4.0
Abstract: Given a graph G and a real number 0≤p≤1, we define the random set Bp(G)⊆V(G) by including each vertex independently and with probability p. We investigate the probability that the random set Bp(G) is a zero forcing set of G. In particular, we prove that for large n, this probability for trees is upper bounded by the corresponding probability for a path graph. Given a minimum degree condition, we also prove a conjecture of Boyer et al. regarding the number of zero forcing sets of a given size that a graph can have.