Jan Florek

collaborators

3 papers

math.CO2025

Kempe equivalence of 4-colourings of some plane triangulations

Jan Florek

Let $G_{n}$ , where $n ⩾ 5$ , be a simple plane triangulation which has $2$ non-adjacent vertices of degree $n$ (called \textit{poles} of $G_{n}$ ) and $2 n$ vertices of degree~$…

math.CO2025

On Dirac and Motzkin problem in discrete geometry

Jan Florek

Dirac and Motzkin conjectured that any set X of $n$ non-collinear points in the plane has an element incident with at least $⌈ \frac{n}{2} ⌉$ lines spanned by X. In this…

math.CO2018

Remarks on Barnette's Conjecture

Jan Florek

Let $P$ be a cubic $3$ -connected bipartite plane graph which has a $2$ -factor which consists only of facial $4$ -cycles, and suppose that $P^{*}$ is the dual graph. We show that $P$ …