2026-09-21T12:49:22Zhttps://iris.unitn.it/oai/requestoai:iris.unitn.it:11572/4066202024-04-30T02:56:34Zcom_11572_237821com_11572_101871col_11572_237822ou_ou00004
Edge-colorings and flows in Class 2 graphs
Tabarelli, Gloria
Tabarelli, Gloria
Graph theory, Edge-colorings, Flows
Settore MAT/03 - Geometria
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.
2024-04-18
info:eu-repo/semantics/doctoralThesis
https://hdl.handle.net/11572/406620
http://dx.doi.org/10.15168/11572_406620
10.15168/11572_406620
eng
firstpage:1
lastpage:125
numberofpages:125
info:eu-repo/semantics/openAccess
Università degli studi di Trento
place:TRENTO
license:Tutti i diritti riservati (All rights reserved)
license uri:iris.PRI01