Edge-colorings and flows in Class 2 graphs

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.

Grantor dc:publisher

Università degli studi di Trento

Year dc:date

2024

Author dc:creator

• Tabarelli, Gloria

• Graph theory, Edge-colorings, Flows
• Settore MAT/03 - Geometria

Statement dc:rights

• info:eu-repo/semantics/openAccess
• license:Tutti i diritti riservati (All rights reserved)
• license uri:iris.PRI01

Language dc:language

eng

Identifier

http://dx.doi.org/10.15168/11572_406620
10.15168/11572_406620

OAI identifier oai:identifier

oai:iris.unitn.it:11572/406620