Probabilistic zero forcing on random graphs

English, Sean; MacRury, Calum; Prałat, Paweł

doi:10.1016/j.ejc.2020.103207

Cited by 7 publications

(9 citation statements)

References 11 publications

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“…[10]), but even with this improvement, the bound is still far from the conjectured value. In [9], the authors explored probabilistic zero forcing on G(n, p) in more detail and, in particular, proved the above conjecture. Their results can be summarized in the following theorem that shows that probabilistic zero forcing occurs much faster in G(n, p) than in a general graph G, as evidenced by the bounds of (1).…”

Section: Results On Probabilistic Zero Forcingmentioning

confidence: 90%

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Tight Bounds on Probabilistic Zero Forcing on Hypercubes and Grids

Behague

Marbach

Prałat

2022

Electron. J. Combin.

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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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Section: Results On Probabilistic Zero Forcingmentioning

confidence: 90%

“…Given a graph G, S, T ⊆ V (G), and ∈ N, let A(S, T, ) be the event that starting with blue set S, after rounds every vertex in T is blue. The following simple observation was proved in [9].…”

Section: Useful Couplingmentioning

confidence: 87%

Tight Bounds on Probabilistic Zero Forcing on Hypercubes and Grids

Behague

Marbach

Prałat

2022

Electron. J. Combin.

Self Cite

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show abstract

“…[8]), but even with this improvement, the bound is still far from the conjectured value. In [7], the authors explored probabilistic zero forcing on G(n, p) in more detail and, in particular, proved the above conjecture. Their results can be summarized in the following theorem that shows that probabilistic zero forcing occurs much faster in G(n, p) than in a general graph G, as evidenced by the bounds of (1.1).…”

mentioning

confidence: 90%

Tight Bounds on the Probabilistic Zero Forcing on Hypercubes and Grids

Behague¹,

Marbach²,

Prałat³

2020

Preprint

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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.In this paper we explore the propagation time for probabilistic zero forcing on hypercubes. This is a preliminary work. We are currently working on grids and some other families of graphs. Stay tuned.

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“…As pointed in [20,26], the forcing process is an instance of a propagation process on graphs, and it has many applications to other branches of mathematics, computer science and physics, such as the linear and quantum controllability for systems that stem from networks [11,12] and the power domination [34]. Moreover, diverse graph processes are employed to model technical or societal processes in other fields.…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, diverse graph processes are employed to model technical or societal processes in other fields. For more details and an overview of the different models and applications, refer to the book [5] and the papers [20,26] with the references therein.…”

Section: Introductionmentioning

confidence: 99%