5 citations · 6 across the 10 of their papers we have counts for
11 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…
Turán problems for oriented graphs
Andrzej Grzesik, Justyna Jaworska, Bartłomiej Kielak +2
A classical Turán problem asks for the maximum possible number of edges in a graph of a given order that does not contain a particular graph as a subgraph. It is well-known tha…
Quasirandom forcing orientations of cycles
Andrzej Grzesik, Daniel Il'kovič, Bartłomiej Kielak +1
An oriented graph is quasirandom-forcing if the limit (homomorphism) density of in a sequence of tournaments is if and only if the sequence is quasirandom. We…
On the inducibility of oriented graphs on four vertices
Łukasz Bożyk, Andrzej Grzesik, Bartłomiej Kielak
We consider the problem of determining the inducibility (maximum possible asymptotic density of induced copies) of oriented graphs on four vertices. We provide exact values for mor…
Exact hyperplane covers for subsets of the hypercube
James Aaronson, Carla Groenland, Andrzej Grzesik +2
Alon and Füredi (1993) showed that the number of hyperplanes required to cover without covering is . We initiate the study of such exact hyperplan…
On the maximum number of odd cycles in graphs without smaller odd cycles
Andrzej Grzesik, Bartłomiej Kielak
We prove that for each odd integer , every graph on vertices without odd cycles of length less than contains at most cycles of length . This generali…