3 papers
math.CO2026
Distribution of independent sets in perfect -ary trees
Daniel Iľkovič, Jun Yan
Given a graph , the family of all independent sets of size containing a fixed vertex is called a star with centre , and is denoted by . Motivated…
math.CO2025
An improved hypergraph Mantel's Theorem
Daniel Iľkovič, Jun Yan
In a recent paper, Chao and Yu used an entropy method to show that the Turán density of a certain family of triangle-like -uniform hypergraphs…
math.CO2024
Multi-cyclic graphs in the random graph process with restricted budget
Daniel Iľkovič, Jared León, Xichao Shu
We study a controlled random graph process introduced by Frieze, Krivelevich, and Michaeli. In this model, the edges of a complete graph are randomly ordered and revealed sequentia…