Jozef Rajn'ik

collaborators

4 papers

math.CO2026

On the $2$ -dimensional flow number of the Flower snarks

Davide Mattiolo, Jozef RajnÃk

Let $r \geq 2$ be a real number, $d$ a positive integer. A $d$ -dimensional nowhere-zero $r$ -flow, or $(r, d)$ -NZF, on a graph $G$ is an orientation of $G$ together with a function $f\…

math.CO2025

Manhattan and Chebyshev flows

LukÃ¡Å¡ GÃ¡borik, Sascha Kurz, Giuseppe Mazzuoccolo +2

We investigate multidimensional nowhere-zero flows of bridgeless graphs. By extending the established use of the Euclidean norm, this paper considers the Manhattan and Chebyshev no…

math.CO2025

Geometric description of $d$ -dimensional flows of a graph

Davide Mattiolo, Giuseppe Mazzuoccolo, Jozef RajnÃk +1

A $d$ -dimensional nowhere-zero $r$ -flow on a graph $G$ , an $(r, d)$ -NZF from now on, is a flow where the value on each edge is an element of $R^{d}$ whose (Euclidean) norm li…

math.CO2025

Cages and cyclic connectivity

Robert LukoÅ¥ka, Edita MÃ¡ÄajovÃ¡, Jozef RajnÃk

A graph $G$ is cyclically $c$ -edge-connected if there is no set of fewer than $c$ edges that disconnects $G$ into at least two cyclic components. We prove that if a $(k, g)$ -cage $…

On the 2-dimensional flow number of the Flower snarks

Manhattan and Chebyshev flows

Geometric description of d-dimensional flows of a graph

Cages and cyclic connectivity

On the $2$ -dimensional flow number of the Flower snarks

Geometric description of $d$ -dimensional flows of a graph