{"id":{"repo_id":"lsu-thes","oai_identifier":"oai:repository.lsu.edu:gradschool_dissertations-1094"},"canonical_url":"https://search.dev.ndltd.org/etd/lsu-thes/oai:repository.lsu.edu:gradschool_dissertations-1094","repository":{"repo_id":"lsu-thes","name":"Lousiana State University","base_url":"https://repository.lsu.edu/do/oai/"},"display":{"title":"Selected Problems on Matroid Minors","abstract":"This dissertation begins with an introduction to matroids and graphs. In the first chapter, we develop matroid and graph theory definitions and preliminary results sufficient to discuss the problems presented in the later chapters. These topics include duality, connectivity, matroid minors, and Cunningham and Edmonds's tree decomposition for connected matroids. One of the most well-known excluded-minor results in matroid theory is Tutte's characterization of binary matroids. The class of binary matroids is one of the most widely studied classes of matroids, and its members have many attractive qualities. This motivates the study of matroid classes that are close to being binary. One very natural such minor-closed class Z consists of those matroids M such that the deletion or the contraction of e is binary for all elements e of M. Chapter 2 is devoted to determining the set of excluded minors for Z. Duality plays a central role in the study of matroids. It is therefore natural to ask the following question: which matroids guarantee that, when present as minors, their duals are present as minors? We answer this question in Chapter 3. We also consider this problem with additional constraints regarding the connectivity and representability of the matroids in question. The main results of Chapter 3 deal with 3-connected matroids.","abstract_html":"This dissertation begins with an introduction to matroids and graphs. In the first chapter, we develop matroid and graph theory definitions and preliminary results sufficient to discuss the problems presented in the later chapters. These topics include duality, connectivity, matroid minors, and Cunningham and Edmonds's tree decomposition for connected matroids. One of the most well-known excluded-minor results in matroid theory is Tutte's characterization of binary matroids. The class of binary matroids is one of the most widely studied classes of matroids, and its members have many attractive qualities. This motivates the study of matroid classes that are close to being binary. One very natural such minor-closed class Z consists of those matroids M such that the deletion or the contraction of e is binary for all elements e of M. Chapter 2 is devoted to determining the set of excluded minors for Z. Duality plays a central role in the study of matroids. It is therefore natural to ask the following question: which matroids guarantee that, when present as minors, their duals are present as minors? We answer this question in Chapter 3. We also consider this problem with additional constraints regarding the connectivity and representability of the matroids in question. The main results of Chapter 3 deal with 3-connected matroids.","abstract_has_math":false,"creators":["Taylor, Jesse"],"institution":"Mathematics","degree_name":"Doctor of Philosophy (PhD)","degree_level":"Dissertation","degree_discipline":"Applied Mathematics","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-01-01T08:00:00Z","date_published":"2014-01-01T08:00:00Z","updated_at":"2026-07-24T02:57:00Z","subjects":["graphs","minors","combinatorics","matroids"],"languages":[],"rights":["unrestricted","Release the entire work immediately for access worldwide."],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["etd-07042014-133808","https://repository.lsu.edu/gradschool_dissertations/95"],"render_values":[{"text":"etd-07042014-133808","href":null,"code":true},{"text":"https://repository.lsu.edu/gradschool_dissertations/95","href":"https://repository.lsu.edu/gradschool_dissertations/95","code":true}]}]},"links":{"outbound_url":"https://doi.org/10.31390/gradschool_dissertations.95","outbound_label":"DOI","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Taylor, Jesse"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2014-06-20"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2022-05-12T23:07:40Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Applied Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy (PhD)"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Mathematics"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["graphs","minors","combinatorics","matroids"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["unrestricted","Release the entire work immediately for access worldwide."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["etd-07042014-133808","10.31390/gradschool_dissertations.95","https://repository.lsu.edu/gradschool_dissertations/95"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["This dissertation begins with an introduction to matroids and graphs. In the first chapter, we develop matroid and graph theory definitions and preliminary results sufficient to discuss the problems presented in the later chapters. These topics include duality, connectivity, matroid minors, and Cunningham and Edmonds's tree decomposition for connected matroids. One of the most well-known excluded-minor results in matroid theory is Tutte's characterization of binary matroids. The class of binary matroids is one of the most widely studied classes of matroids, and its members have many attractive qualities. This motivates the study of matroid classes that are close to being binary. One very natural such minor-closed class Z consists of those matroids M such that the deletion or the contraction of e is binary for all elements e of M. Chapter 2 is devoted to determining the set of excluded minors for Z. Duality plays a central role in the study of matroids. It is therefore natural to ask the following question: which matroids guarantee that, when present as minors, their duals are present as minors? We answer this question in Chapter 3. We also consider this problem with additional constraints regarding the connectivity and representability of the matroids in question. The main results of Chapter 3 deal with 3-connected matroids."]},{"key":"dc:title","label":"Title","values":["Selected Problems on Matroid Minors"]}]}],"canonical_facts":{"dc:creator":["Taylor, Jesse"],"dc:date":["2014-06-20"],"dc:date.available":["2022-05-12T23:07:40Z"],"dc:description.abstract":["This dissertation begins with an introduction to matroids and graphs. In the first chapter, we develop matroid and graph theory definitions and preliminary results sufficient to discuss the problems presented in the later chapters. These topics include duality, connectivity, matroid minors, and Cunningham and Edmonds's tree decomposition for connected matroids. One of the most well-known excluded-minor results in matroid theory is Tutte's characterization of binary matroids. The class of binary matroids is one of the most widely studied classes of matroids, and its members have many attractive qualities. This motivates the study of matroid classes that are close to being binary. One very natural such minor-closed class Z consists of those matroids M such that the deletion or the contraction of e is binary for all elements e of M. Chapter 2 is devoted to determining the set of excluded minors for Z. Duality plays a central role in the study of matroids. It is therefore natural to ask the following question: which matroids guarantee that, when present as minors, their duals are present as minors? We answer this question in Chapter 3. We also consider this problem with additional constraints regarding the connectivity and representability of the matroids in question. The main results of Chapter 3 deal with 3-connected matroids."],"dc:identifier":["etd-07042014-133808","10.31390/gradschool_dissertations.95","https://repository.lsu.edu/gradschool_dissertations/95"],"dc:rights":["unrestricted","Release the entire work immediately for access worldwide."],"dc:subject":["graphs","minors","combinatorics","matroids"],"dc:title":["Selected Problems on Matroid Minors"],"thesis:degree_discipline":["Applied Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Doctor of Philosophy (PhD)"],"thesis:institution_name":["Mathematics"]},"updated_at":"2026-07-24T02:57:00Z"}