Edge-colorings and flows in Class 2 graphs

Cycle 36th Oral Defence of the Phd Thesis
18 April 2024
Start time 
11:00 am
PovoZero - Via Sommarive 14, Povo (Trento)
Seminar Room – Department of Physics – Povo 0
Doctoral School in Mathematics
Target audience: 
University community
Online – Registration required
Registration email: 
Contact person: 
Giuseppe Mazzuoccolo - Peter Schuster

Tabarelli Gloria - PhD in Mathematics, University of Trento

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 statement of 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 finally 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.