Seminár z teórie grafov - Jozef Rajník (27.2.2025)
vo štvrtok 27.2.2025 o 9:50 hod. v miestnosti M 213
Prednášajúci: Jozef Rajník
Názov: On lower bounds on d-dimensional flow numbers
Termín: 27.2.2025, 9:50 hod., M 213
Abstrakt:
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.