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

Enumeration of plane triangulations with all vertices of degree $3$ or $6$ and a new characterization of akempic triangulations

Jan Florek

Plane triangulations with all vertices of degree $3$ or $6$ are enumerated. A plane triangulation is said to be akempic if it has a $4$ -colouring such that no two adjacent triangle…

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…

Kempe equivalence of 4-colourings of some plane triangulations

Enumeration of plane triangulations with all vertices of degree 3 or 6 and a new characterization of akempic triangulations

On Dirac and Motzkin problem in discrete geometry

Enumeration of plane triangulations with all vertices of degree $3$ or $6$ and a new characterization of akempic triangulations