Abstract
dc:descriptionWe 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.
Degree
thesis:*- Grantor dc:publisher
- Università degli studi di Trento
- Year dc:date
- 2024
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Tabarelli, Gloria
Subjects
dc:subject × 2Rights
dc:rights- Statement dc:rights
-
- info:eu-repo/semantics/openAccess
- license:Tutti i diritti riservati (All rights reserved)
- license uri:iris.PRI01
- Language dc:language
- eng
Identifiers
dc:identifier.*- OAI identifier oai:identifier
- oai:iris.unitn.it:11572/406620