Random Set Zero Forcing (Spring 2023)

Consider a graph G with vertices initially colored blue or white. Zero forcing can be described as a graph coloring game that follows a single rule: If a blue vertex has exactly one white neighbor, then we may change its color to blue. If an initial set of blue vertices B can eventually turn every vertex of G blue, then we say that B is a zero forcing set. In this project we will investigate the probability that a random set of vertices is a zero forcing set. This variant of zero forcing, called random set zero forcing, was introduced in a recent paper and has many avenues left for exploration. Problems that students can work on include:

• writing code to investigate random set zero forcing,

• compute threshold probabilities for various families of graphs,

• investigate new questions such as: what is the probability that a random set of size k is a zero forcing set?

For more information contact Brian Curtis (bcurtis1@iastate.edu)

People:

• Brian Curtis (Postdoc)

• Zachary Brennan (Grad)

• Ben Cohen (UGrad)

• Joseph Jonasson (UGrad)

• Henry Simmons (UGrad)

Pre-requisites:

• Experience writing proofs

• Experience in probability (MATH 104 or higher) is desirable but not required

• Experience in combinatorics (MATH 304) is desirable but not required

• Experience with programming (e.g. python, sage or Mathematica) is desirable but not required