Tight Bounds on Probabilistic Zero Forcing on Hypercubes and Grids

  • Natalie C. Behague
  • Trent G. Marbach
  • Paweł Prałat


Zero forcing is a deterministic iterative graph colouring process in which vertices are coloured either blue or white, and in every round, any blue vertices that have a single white neighbour force these white vertices to become blue. Here we study probabilistic zero forcing, where blue vertices have a non-zero probability of forcing each white neighbour to become blue. We explore the propagation time for probabilistic zero forcing on hypercubes and grids.

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