## Probability recurrences on simple graphs in a forest building process

 dc.contributor.author Alameda, Joseph dc.contributor.department Mathematics dc.contributor.majorProfessor Steve Butler dc.date 2019-09-19T05:54:13.000 dc.date.accessioned 2020-06-30T01:32:31Z dc.date.available 2020-06-30T01:32:31Z dc.date.copyright Tue Jan 01 00:00:00 UTC 2019 dc.date.issued 2019-01-01 dc.description.abstract

Consider the following process on a simple graph with no isolated vertices: Randomly order the edges and remove an edge if and only if the edge is incident to two vertices already incident to some preceding edge. This process results in a spanning forest of the graph.

Recurrences are given for the process for multiple families of graphs, and the probability of obtaining \$k\$ components in the above process is given by a new method for the Fan graph \$F_{n-2,2}\$. An approach to proving a previously published conjecture is also discussed.

dc.format.mimetype application/pdf dc.identifier archive/lib.dr.iastate.edu/creativecomponents/125/ dc.identifier.articleid 1171 dc.identifier.contextkey 14233929 dc.identifier.s3bucket isulib-bepress-aws-west dc.identifier.submissionpath creativecomponents/125 dc.identifier.uri https://dr.lib.iastate.edu/handle/20.500.12876/16652 dc.source.bitstream archive/lib.dr.iastate.edu/creativecomponents/125/AlamedaCreative.pdf|||Fri Jan 14 19:23:17 UTC 2022 dc.subject.disciplines Discrete Mathematics and Combinatorics dc.subject.keywords graphs dc.subject.keywords forests dc.subject.keywords trees dc.subject.keywords recurrence dc.subject.keywords probability dc.title Probability recurrences on simple graphs in a forest building process dc.type article dc.type.genre creativecomponent dspace.entity.type Publication relation.isOrgUnitOfPublication 82295b2b-0f85-4929-9659-075c93e82c48 thesis.degree.discipline Mathematics thesis.degree.level creativecomponent
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