{"id":{"repo_id":"trento","oai_identifier":"oai:iris.unitn.it:11572/406620"},"canonical_url":"https://search.dev.ndltd.org/etd/trento/oai:iris.unitn.it:11572/406620","repository":{"repo_id":"trento","name":"Università degli Studi di Trento","base_url":"https://iris.unitn.it/oai/request"},"display":{"title":"Edge-colorings and flows in Class 2 graphs","abstract":"We consider edge-colorings and flows problems in Graph Theory that are hard to solve for Class 2 graphs. Most of them are strongly related to some outstanding open conjectures, such as the Cycle Double Cover Conjecture, the Berge-Fulkerson Conjecture, the Petersen Coloring Conjecture and the Tutte's 5-flow Conjecture. We obtain some new restrictions on the structure of a possible minimum counterexample to the former two conjectures. We prove that the Petersen graph is, in a specific sense, the only graph that could appear in the Petersen Coloring Conjecture, and we provide evidence that led to propose an analogous of the Tutte's 5-flow conjecture in higher dimensions. We prove a characterization result and a sufficient condition for general graphs in relation to another edge-coloring problem, which is the determination of the palette index of a graph.","abstract_html":"We consider edge-colorings and flows problems in Graph Theory that are hard to solve for Class 2 graphs. Most of them are strongly related to some outstanding open conjectures, such as the Cycle Double Cover Conjecture, the Berge-Fulkerson Conjecture, the Petersen Coloring Conjecture and the Tutte's 5-flow Conjecture. We obtain some new restrictions on the structure of a possible minimum counterexample to the former two conjectures. We prove that the Petersen graph is, in a specific sense, the only graph that could appear in the Petersen Coloring Conjecture, and we provide evidence that led to propose an analogous of the Tutte's 5-flow conjecture in higher dimensions. We prove a characterization result and a sufficient condition for general graphs in relation to another edge-coloring problem, which is the determination of the palette index of a graph.","abstract_has_math":false,"creators":["Tabarelli, Gloria"],"institution":"Università degli studi di Trento","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2024,"date_issued":"2024-04-18","date_published":"2024-04-18","updated_at":"2026-07-24T05:04:40Z","subjects":["Graph theory, Edge-colorings, Flows","Settore MAT/03 - Geometria"],"languages":["eng"],"rights":["info:eu-repo/semantics/openAccess","license:Tutti i diritti riservati (All rights reserved)","license uri:iris.PRI01"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["http://dx.doi.org/10.15168/11572_406620","10.15168/11572_406620"],"render_values":[{"text":"http://dx.doi.org/10.15168/11572_406620","href":"http://dx.doi.org/10.15168/11572_406620","code":true},{"text":"10.15168/11572_406620","href":"https://doi.org/10.15168/11572_406620","code":true}]}]},"links":{"outbound_url":"https://hdl.handle.net/11572/406620","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Tabarelli, Gloria"]},{"key":"dc:creator","label":"Author","values":["Tabarelli, Gloria"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2024-04-18"]},{"key":"dc:publisher","label":"Institution","values":["Università degli studi di Trento","place:TRENTO"]},{"key":"dc:relation","label":"Dc Relation","values":["firstpage:1","lastpage:125","numberofpages:125"]},{"key":"dc:type","label":"Dc Type","values":["info:eu-repo/semantics/doctoralThesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Graph theory, Edge-colorings, Flows","Settore MAT/03 - Geometria"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["info:eu-repo/semantics/openAccess","license:Tutti i diritti riservati (All rights reserved)","license uri:iris.PRI01"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://hdl.handle.net/11572/406620","http://dx.doi.org/10.15168/11572_406620","10.15168/11572_406620"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["We consider edge-colorings and flows problems in Graph Theory that are hard to solve for Class 2 graphs. Most of them are strongly related to some outstanding open conjectures, such as the Cycle Double Cover Conjecture, the Berge-Fulkerson Conjecture, the Petersen Coloring Conjecture and the Tutte's 5-flow Conjecture. We obtain some new restrictions on the structure of a possible minimum counterexample to the former two conjectures. We prove that the Petersen graph is, in a specific sense, the only graph that could appear in the Petersen Coloring Conjecture, and we provide evidence that led to propose an analogous of the Tutte's 5-flow conjecture in higher dimensions. We prove a characterization result and a sufficient condition for general graphs in relation to another edge-coloring problem, which is the determination of the palette index of a graph."]},{"key":"dc:title","label":"Title","values":["Edge-colorings and flows in Class 2 graphs"]}]}],"canonical_facts":{"dc:contributor":["Tabarelli, Gloria"],"dc:creator":["Tabarelli, Gloria"],"dc:date":["2024-04-18"],"dc:description":["We consider edge-colorings and flows problems in Graph Theory that are hard to solve for Class 2 graphs. Most of them are strongly related to some outstanding open conjectures, such as the Cycle Double Cover Conjecture, the Berge-Fulkerson Conjecture, the Petersen Coloring Conjecture and the Tutte's 5-flow Conjecture. We obtain some new restrictions on the structure of a possible minimum counterexample to the former two conjectures. We prove that the Petersen graph is, in a specific sense, the only graph that could appear in the Petersen Coloring Conjecture, and we provide evidence that led to propose an analogous of the Tutte's 5-flow conjecture in higher dimensions. We prove a characterization result and a sufficient condition for general graphs in relation to another edge-coloring problem, which is the determination of the palette index of a graph."],"dc:identifier":["https://hdl.handle.net/11572/406620","http://dx.doi.org/10.15168/11572_406620","10.15168/11572_406620"],"dc:language":["eng"],"dc:publisher":["Università degli studi di Trento","place:TRENTO"],"dc:relation":["firstpage:1","lastpage:125","numberofpages:125"],"dc:rights":["info:eu-repo/semantics/openAccess","license:Tutti i diritti riservati (All rights reserved)","license uri:iris.PRI01"],"dc:subject":["Graph theory, Edge-colorings, Flows","Settore MAT/03 - Geometria"],"dc:title":["Edge-colorings and flows in Class 2 graphs"],"dc:type":["info:eu-repo/semantics/doctoralThesis"]},"updated_at":"2026-07-24T05:04:40Z"}