Jan Florek

activity

20182025

collaborators

6 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.RT2025

Relative Serre duality for Hecke categories

Quoc P. Ho, Penghui Li

We prove a conjecture of Gorsky, Hogancamp, Mellit, and Nakagane in the Weyl group case. Namely, we show that the left and right adjoints of the parabolic induction functor between…

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.CO2023

The Stein theorem for loopless 2-connected plane multigraphs

Jan Florek

Stein proved that for each simple plane triangulation H there exists a partitioning of the vertex of H into two subsets each of which induces a forest if and only if the dual H^{*}…

math.CO2023

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.…

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 $P$ …