Jan Florek

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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…

math.CO2024

A sufficient condition for cubic 3-connected plane bipartite graphs to be hamiltonian

Jan Florek

Barnette's conjecture asserts that every cubic $3$ -connected plane bipartite graph is hamiltonian. Although, in general, the problem is still open, some partial results are known.…

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

A sufficient condition for cubic 3-connected plane bipartite graphs to be hamiltonian

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