{"id":{"repo_id":"western-cape","oai_identifier":"oai:uwcscholar.uwc.ac.za:10566/23135"},"canonical_url":"https://search.dev.ndltd.org/etd/western-cape/oai:uwcscholar.uwc.ac.za:10566/23135","repository":{"repo_id":"western-cape","name":"University of the Western Cape","base_url":"https://uwcscholar.uwc.ac.za:8443/server/oai/request"},"display":{"title":"Measurements of edge uncolourability in cubic graphs","abstract":"The history of the pursuit of uncolourable cubic graphs dates back more than a century. This pursuit has evolved from the slow discovery of individual uncolourable cubic graphs such as the famous Petersen graph and the Blanusa snarks, to discovering in nite classes of uncolourable cubic graphs such as the Louphekine and Goldberg snarks, to investigating parameters which measure the uncolourability of cubic graphs. These parameters include resistance, oddness and weak oddness, ow resistance, among others. In this thesis, we consider current ideas and problems regarding the uncolourability of cubic graphs, centering around these parameters. We introduce new ideas regarding the structural complexity of these graphs in question. In particular, we consider their 3-critical subgraphs, speci cally in relation to resistance. We further introduce new parameters which measure the uncolourability of cubic graphs, speci cally relating to their 3-critical subgraphs and various types of cubic graph reductions. This is also done with a view to identifying further problems of interest. This thesis also presents solutions and partial solutions to long-standing open conjectures relating in particular to oddness, weak oddness and resistance.","abstract_html":"The history of the pursuit of uncolourable cubic graphs dates back more than a century. This pursuit has evolved from the slow discovery of individual uncolourable cubic graphs such as the famous Petersen graph and the Blanusa snarks, to discovering in nite classes of uncolourable cubic graphs such as the Louphekine and Goldberg snarks, to investigating parameters which measure the uncolourability of cubic graphs. These parameters include resistance, oddness and weak oddness, ow resistance, among others. In this thesis, we consider current ideas and problems regarding the uncolourability of cubic graphs, centering around these parameters. We introduce new ideas regarding the structural complexity of these graphs in question. In particular, we consider their 3-critical subgraphs, speci cally in relation to resistance. We further introduce new parameters which measure the uncolourability of cubic graphs, speci cally relating to their 3-critical subgraphs and various types of cubic graph reductions. This is also done with a view to identifying further problems of interest. This thesis also presents solutions and partial solutions to long-standing open conjectures relating in particular to oddness, weak oddness and resistance.","abstract_has_math":false,"creators":["Allie, Imran"],"institution":"University of the Western Cape","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2020,"date_issued":"2020","date_published":"2020","updated_at":"2026-07-24T06:00:54Z","subjects":["Cubic graphs","Petersen graph","Blanusa snarks","Uncolourability","Oddness"],"languages":[],"rights":[],"rights_urls":["https://uwcscholar.uwc.ac.za/bitstreams/311bbe8e-8303-4d25-8074-587856eac1d2/download"],"identifier_entries":[]},"links":{"outbound_url":null,"outbound_label":null,"outbound_source":null},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Allie, Imran"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.issued","label":"Date","values":["2020"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["University of the Western Cape"]},{"key":"dc:relation.isreferencedby","label":"Dc Relation Isreferencedby","values":["https://hdl.handle.net/10566/23135"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Cubic graphs","Petersen graph","Blanusa snarks","Uncolourability","Oddness"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["https://uwcscholar.uwc.ac.za/bitstreams/311bbe8e-8303-4d25-8074-587856eac1d2/download"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://uwcscholar.uwc.ac.za/bitstreams/17737583-7e7c-47a9-951e-28c84fb11579/download"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The history of the pursuit of uncolourable cubic graphs dates back more than a century. This pursuit has evolved from the slow discovery of individual uncolourable cubic graphs such as the famous Petersen graph and the Blanusa snarks, to discovering in nite classes of uncolourable cubic graphs such as the Louphekine and Goldberg snarks, to investigating parameters which measure the uncolourability of cubic graphs. These parameters include resistance, oddness and weak oddness, ow resistance, among others. In this thesis, we consider current ideas and problems regarding the uncolourability of cubic graphs, centering around these parameters. We introduce new ideas regarding the structural complexity of these graphs in question. In particular, we consider their 3-critical subgraphs, speci cally in relation to resistance. We further introduce new parameters which measure the uncolourability of cubic graphs, speci cally relating to their 3-critical subgraphs and various types of cubic graph reductions. This is also done with a view to identifying further problems of interest. This thesis also presents solutions and partial solutions to long-standing open conjectures relating in particular to oddness, weak oddness and resistance."]},{"key":"dc:format.checksum.md5","label":"Dc Format Checksum Md5","values":["06eed93c7433b842326425e598ce5dd1","bb9bdc0b3349e4284e09149f943790b4","aba38c32fd881cbe157b76b701430e55"]},{"key":"dc:title","label":"Title","values":["Measurements of edge uncolourability in cubic graphs"]}]}],"canonical_facts":{"dc:creator":["Allie, Imran"],"dc:date.issued":["2020"],"dc:description.abstract":["The history of the pursuit of uncolourable cubic graphs dates back more than a century. This pursuit has evolved from the slow discovery of individual uncolourable cubic graphs such as the famous Petersen graph and the Blanusa snarks, to discovering in nite classes of uncolourable cubic graphs such as the Louphekine and Goldberg snarks, to investigating parameters which measure the uncolourability of cubic graphs. These parameters include resistance, oddness and weak oddness, ow resistance, among others. In this thesis, we consider current ideas and problems regarding the uncolourability of cubic graphs, centering around these parameters. We introduce new ideas regarding the structural complexity of these graphs in question. In particular, we consider their 3-critical subgraphs, speci cally in relation to resistance. We further introduce new parameters which measure the uncolourability of cubic graphs, speci cally relating to their 3-critical subgraphs and various types of cubic graph reductions. This is also done with a view to identifying further problems of interest. This thesis also presents solutions and partial solutions to long-standing open conjectures relating in particular to oddness, weak oddness and resistance."],"dc:format.checksum.md5":["06eed93c7433b842326425e598ce5dd1","bb9bdc0b3349e4284e09149f943790b4","aba38c32fd881cbe157b76b701430e55"],"dc:identifier.uri":["https://uwcscholar.uwc.ac.za/bitstreams/17737583-7e7c-47a9-951e-28c84fb11579/download"],"dc:publisher.institution":["University of the Western Cape"],"dc:relation.isreferencedby":["https://hdl.handle.net/10566/23135"],"dc:rights":["https://uwcscholar.uwc.ac.za/bitstreams/311bbe8e-8303-4d25-8074-587856eac1d2/download"],"dc:subject":["Cubic graphs","Petersen graph","Blanusa snarks","Uncolourability","Oddness"],"dc:title":["Measurements of edge uncolourability in cubic graphs"],"dc:type":["Thesis"]},"updated_at":"2026-07-24T06:00:54Z"}