4 papers · 1 filter
Turán Problems for Small Tournaments and Stability
Daniel Iľkovič
We investigate the Turán problems for various small directed graphs, specifically focusing on self-converse tournaments and stability versions. First, we determine the exact…
Arithmetic progressions in a random set on a budget
Jan Hladký, Daniel Iľkovič, Jared León +1
A restricted-budget version of the random graph process, introduced by Frieze, Krivelevich, and Michaeli in 2025, studies the construction of structures by an online player who can…
On cospectral graphons
Jan Hladký, Daniel Iľkovič, Jared León +1
In this short note, we introduce cospectral graphons, paralleling the notion of cospectral graphs. As in the graph case, we give three equivalent definitions: by equality of spectr…
Hypergraphs with uniform Turán density equal to 8/27
Frederik Garbe, Daniel Iľkovič, Daniel Kráľ +2
In the 1980s, Erdős and Sós initiated the study of Turán problems with a uniformity condition on the distribution of edges: the uniform Turán density of a hypergraph is the inf…