7 papers
Solution of uniform Turán's Tetrahedron Problem
Bartłomiej Kielak, Daniel Král, Ander Lamaison +3
Turán's Tetrahedron Problem asks to determine the Turán density of the complete hypergraph (tetrahedron). This problem, posed by Turán in 1941, is one of the most famou…
Fundamental cycles in grid graphs
Bartłomiej Kielak, Daniel Král', Ander Lamaison +1
We show that the average length of a fundamental cycle with respect to any fixed spanning tree of the square grid is at least ; the bound is asymptotically t…
Constricting the Computational Complexity Gap of the -Coloring Problem in -free Graphs
Justyna Jaworska, Bartłomiej Kielak, Tomáš Masařík +1
The -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…
Generalized Turán problem for directed cycles
Andrzej Grzesik, Justyna Jaworska, Bartłomiej Kielak +2
For integers , let denote the maximum number of directed cycles of length in any oriented graph…
The generalized trifference problem
Anurag Bishnoi, Bartłomiej Kielak, Benedek Kovács +4
We study the problem of finding the largest number of ternary vectors of length such that for any three distinct vectors there are at least coordinates where they…
Curves on the torus with few intersections
Igor Balla, Marek Filakovský, Bartłomiej 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…