Bartłomiej Kielak

collaborators

5 papers

math.CO2026

Fundamental cycles in grid graphs

BartÅomiej Kielak, Bartłomiej Kielak, Daniel KrÃ¡l' +3

We show that the average length of a fundamental cycle with respect to any fixed spanning tree of the $n \times n$ square grid is at least $Ω (lo g n)$ ; the bound is asymptotically t…

math.CO2026

Curves on the torus with few intersections

Igor Balla, Marek FilakovskÃ½, BartÅomiej Kielak +2

Aougab and Gaster [Math. Proc. Cambridge Philos. Soc. 174 (2023), 569-584] proved that any set of simple closed curves on the torus, where any two are non-homotopic and intersect a…

cs.CC2025

Constricting the Computational Complexity Gap of the $4$ -Coloring Problem in $(P_{t}, C_{3})$ -free Graphs

Justyna Jaworska, BartÅomiej Kielak, TomÃ¡Å¡ MasaÅÃk +1

The $k$ -Coloring problem on hereditary graph classes has been a deeply researched problem over the last decade. A hereditary graph class is characterized by a (possibly infinite) l…

math.CO2025

Generalized TurÃ¡n problem for directed cycles

Andrzej Grzesik, Justyna Jaworska, BartÅomiej Kielak +2

For integers $k, ℓ \geq 3$ , let $ex (n, C_{k}, C_{ℓ})$ denote the maximum number of directed cycles of length $k$ in any oriented graph…

math.CO2025

The generalized trifference problem

Anurag Bishnoi, BartÅomiej Kielak, Benedek KovÃ¡cs +4

We study the problem of finding the largest number $T (n, m)$ of ternary vectors of length $n$ such that for any three distinct vectors there are at least $m$ coordinates where they…