{"id":{"repo_id":"mississippi","oai_identifier":"oai:egrove.olemiss.edu:etd-1667"},"canonical_url":"https://search.dev.ndltd.org/etd/mississippi/oai:egrove.olemiss.edu:etd-1667","repository":{"repo_id":"mississippi","name":"University of Mississippi","base_url":"https://egrove.olemiss.edu/do/oai/"},"display":{"title":"Ramsey Theory Using Matroid Minors","abstract":"This thesis considers a Ramsey Theory question for graphs and regular matroids. Specifically, how many elements N are required in a 3-connected graphic or regular matroid to force the existence of certain specified minors in that matroid? This question cannot be answered for an arbitrary collection of specified minors. However, there are results from the literature for which the number N exists for certain collections of minors. We first encode totally unimodular matrix representations of certain matroids. We use the computer program MACEK to investigate this question for certain classes of specified minors.","abstract_html":"This thesis considers a Ramsey Theory question for graphs and regular matroids. Specifically, how many elements N are required in a 3-connected graphic or regular matroid to force the existence of certain specified minors in that matroid? This question cannot be answered for an arbitrary collection of specified minors. However, there are results from the literature for which the number N exists for certain collections of minors. We first encode totally unimodular matrix representations of certain matroids. We use the computer program MACEK to investigate this question for certain classes of specified minors.","abstract_has_math":false,"creators":["Horne, Dixie Smith"],"institution":null,"degree_name":"M.A. in Mathematics","degree_level":"Thesis","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Talmadge James Reid","Stanislaw M. Dziobiak","Haidong Wu"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-01-01T08:00:00Z","date_published":"2014-01-01T08:00:00Z","updated_at":"2026-07-24T03:05:53Z","subjects":["Graphic Matroid","Matroid Theory","Ramsey Theory","Regular Matroid","Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://egrove.olemiss.edu/etd/668","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Talmadge James Reid","Stanislaw M. 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Specifically, how many elements N are required in a 3-connected graphic or regular matroid to force the existence of certain specified minors in that matroid? This question cannot be answered for an arbitrary collection of specified minors. However, there are results from the literature for which the number N exists for certain collections of minors. We first encode totally unimodular matrix representations of certain matroids. We use the computer program MACEK to investigate this question for certain classes of specified minors."]},{"key":"dc:title","label":"Title","values":["Ramsey Theory Using Matroid Minors"]}]}],"canonical_facts":{"dc:contributor":["Talmadge James Reid","Stanislaw M. Dziobiak","Haidong Wu"],"dc:creator":["Horne, Dixie Smith"],"dc:date.available":["2019-06-20T07:00:00Z"],"dc:description.abstract":["This thesis considers a Ramsey Theory question for graphs and regular matroids. Specifically, how many elements N are required in a 3-connected graphic or regular matroid to force the existence of certain specified minors in that matroid? This question cannot be answered for an arbitrary collection of specified minors. However, there are results from the literature for which the number N exists for certain collections of minors. We first encode totally unimodular matrix representations of certain matroids. We use the computer program MACEK to investigate this question for certain classes of specified minors."],"dc:identifier":["https://egrove.olemiss.edu/etd/668"],"dc:subject":["Graphic Matroid","Matroid Theory","Ramsey Theory","Regular Matroid","Mathematics"],"dc:title":["Ramsey Theory Using Matroid Minors"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["M.A. in Mathematics"]},"updated_at":"2026-07-24T03:05:53Z"}