{"id":{"repo_id":"brock","oai_identifier":"oai:brocku.scholaris.ca:10464/5004"},"canonical_url":"https://search.dev.ndltd.org/etd/brock/oai:brocku.scholaris.ca:10464/5004","repository":{"repo_id":"brock","name":"Brock University","base_url":"https://brocku.scholaris.ca/server/oai/request"},"display":{"title":"Edge-choosability of Planar Graphs","abstract":"According to the List Colouring Conjecture, if G is a multigraph then χ' (G)=χl' (G) . In this thesis, we discuss a relaxed version of this conjecture that every simple graph G is edge-(∆ + 1)-choosable as by Vizing’s Theorem ∆(G) ≤χ' (G)≤∆(G) + 1. We prove that if G is a planar graph without 7-cycles with ∆(G)≠5,6 , or without adjacent 4-cycles with ∆(G)≠5, or with no 3-cycles adjacent to 5-cycles, then G is edge-(∆ + 1)-choosable.","abstract_html":"According to the List Colouring Conjecture, if G is a multigraph then χ' (G)=χl' (G) . In this thesis, we discuss a relaxed version of this conjecture that every simple graph G is edge-(∆ + 1)-choosable as by Vizing’s Theorem ∆(G) ≤χ' (G)≤∆(G) + 1. We prove that if G is a planar graph without 7-cycles with ∆(G)≠5,6 , or without adjacent 4-cycles with ∆(G)≠5, or with no 3-cycles adjacent to 5-cycles, then G is edge-(∆ + 1)-choosable.","abstract_has_math":false,"creators":["Mashhadi Avaz Tehrani, Hediyeh"],"institution":"Brock University","degree_name":"M.Sc. 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We prove that if G is a planar graph without 7-cycles with ∆(G)≠5,6 , or without adjacent 4-cycles with ∆(G)≠5, or with no 3-cycles adjacent to 5-cycles, then G is edge-(∆ + 1)-choosable."]},{"key":"dc:title","label":"Title","values":["Edge-choosability of Planar Graphs"]}]}],"canonical_facts":{"dc:contributor.department":["Department of Mathematics"],"dc:creator":["Mashhadi Avaz Tehrani, Hediyeh"],"dc:date.accessioned":["2013-09-26T19:58:50Z"],"dc:date.available":["2013-09-26T19:58:50Z"],"dc:date.issued":["2013-09-26"],"dc:description.abstract":["According to the List Colouring Conjecture, if G is a multigraph then χ' (G)=χl' (G) . In this thesis, we discuss a relaxed version of this conjecture that every simple graph G is edge-(∆ + 1)-choosable as by Vizing’s Theorem ∆(G) ≤χ' (G)≤∆(G) + 1. We prove that if G is a planar graph without 7-cycles with ∆(G)≠5,6 , or without adjacent 4-cycles with ∆(G)≠5, or with no 3-cycles adjacent to 5-cycles, then G is edge-(∆ + 1)-choosable."],"dc:identifier.uri":["http://hdl.handle.net/10464/5004"],"dc:language.iso":["eng"],"dc:subject":["Edge-choosability, List-edge-colouring, Planar graphs"],"dc:title":["Edge-choosability of Planar Graphs"],"dc:type":["Electronic Thesis or Dissertation"],"thesis:degree_discipline":["Faculty of Mathematics and Science"],"thesis:degree_level":["Masters"],"thesis:degree_name":["M.Sc. Mathematics and Statistics"],"thesis:institution_name":["Brock University"]},"updated_at":"2026-07-24T01:23:12Z"}