Minimum Conditions for Bootstrap Percolation on the Cubic Graph

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dc.contributor.advisorFerrero, Daniela
dc.contributor.authorSchlortt, Casey Quinn
dc.date.accessioned2020-07-20T18:34:05Z
dc.date.available2020-07-20T18:34:05Z
dc.date.issued2020-05
dc.description.abstractBootstrap percolation is an iterative process on the vertices of a graph. Initially, a proper, non-empty set of vertices is infected, and all other vertices are uninfected. At each iteration, every uninfected vertex with a certain number of infected neighbors becomes infected, and all infected vertices remain so permanently. At the end of the process, if all vertices are infected, percolation occurs. In this case, the initial set of infected vertices percolates the graph. Necessary and sufficient conditions for the minimum size of a percolating set and the minimum number of rounds to achieve percolation on a cubic graph of order 2n are presented, for any integer n, 2n ≥ 4.
dc.description.departmentHonors College
dc.formatText
dc.format.extent21 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationSchlortt, C. Q. (2020). Minimum conditions for bootstrap percolation on the cubic graph (Unpublished thesis). Texas State University, San Marcos, Texas.
dc.identifier.urihttps://hdl.handle.net/10877/12126
dc.language.isoen
dc.subjectbootstrap percolation
dc.subjectcubic graphs
dc.subject3-regular graphs
dc.subjectiterative process
dc.subject2-neighbor bootstrap percolation
dc.subjectmajority bootstrap percolation
dc.subjectminimum percolating set cardinality
dc.subjectminimum number of rounds
dc.subjectHonors College
dc.titleMinimum Conditions for Bootstrap Percolation on the Cubic Graph
thesis.degree.departmentHonors College
thesis.degree.disciplineMathematics
thesis.degree.grantorTexas State University
txstate.documenttypeHonors Thesis

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