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Ramsey regions and simplicial homology tables for graphs

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dc.contributor.authorFrederick, Christopher Austin, author
dc.contributor.authorPeterson, Chris, advisor
dc.date.accessioned2024-03-13T19:26:18Z
dc.date.available2024-03-13T19:26:18Z
dc.date.issued2008
dc.description.abstractRamsey Theory is the investigation of edge-colored graphs which force a monochromatic subgraph. We devise a way of breaking certain Ramsey Theory problems into "smaller" pieces so that information about Ramsey Theory can be gained without solving the entire problem, (which is often difficult to solve). Next the work with Ramsey Regions for graphs is translated into the language of hypergraphs. Theorems and techniques are reworked to fit appropriately into the setting of hypergraphs. The work of persistence complex on large data sets is examined in the setting of graphs. Various simplicial complexes can be assigned to a graph. For a given simplicial complex the persistence complex can be constructed, giving a highly detailed graph invariant. Connections between the graph and persistence complex are investigated.
dc.format.mediumborn digital
dc.format.mediumdoctoral dissertations
dc.identifierETDF_Frederick_2008_3346425.pdf
dc.identifier.urihttps://hdl.handle.net/10217/237737
dc.languageEnglish
dc.language.isoeng
dc.publisherColorado State University. Libraries
dc.relation.ispartof2000-2019
dc.rightsCopyright and other restrictions may apply. User is responsible for compliance with all applicable laws. For information about copyright law, please see https://libguides.colostate.edu/copyright.
dc.rights.licensePer the terms of a contractual agreement, all use of this item is limited to the non-commercial use of Colorado State University and its authorized users.
dc.subjectgraph theory
dc.subjecthomology tables
dc.subjectRamsey regions
dc.subjectmathematics
dc.titleRamsey regions and simplicial homology tables for graphs
dc.typeText
dcterms.rights.dplaThis Item is protected by copyright and/or related rights (https://rightsstatements.org/vocab/InC/1.0/). You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
thesis.degree.disciplineMathematics
thesis.degree.grantorColorado State University
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy (Ph.D.)

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