Seminar of Graph Theory - Jozef Rajník (27.2.2025)
Thursday 27.2.2025 at 9:50, Lecture room M 213
Jozef Rajník:
On lower bounds on d-dimensional flow numbers
Abstract:
A d-dimensional nowhere-zero r-flow on a graph G, an (r,d)-NZF for short, is a flow where the value on each edge is an element of R^d whose (Euclidean) norm lies in the interval [1,r-1]. The d-dimensional flow number of a bridgeless graph is the minimal r for which G has an (r,d)-NZF. We have introduced this notion generalising integer, circular and unit vector flows. It turns out that obtaining lower bounds of d-dimensional flow numbers is a difficult task, even for specific small graphs such as the Petersen graph. Thus, in this talk, we present two non-trivial lower bounds we have obtained – for the wheel graphs and the Isaacs flower snarks. The former implies a lower bound for any cubic graph depending on its odd-girth.
This is a joint work with Davide Mattiolo, Giuseppe Mazzuoccolo and Gloria Tabarelli. The author of this talk is supported by grants VEGA 1/0727/22 and APVV-23-0076.