G. Katona

collaborators

11 papers

math.CO2026

Multiplicity for partially ordered sets

Gyula O. H. Katona, Yaping Mao

Let $Q = {Q_{a} : a \geq 1}$ be a nested family of finite posets such that $Q_{a} \subseteq Q_{a + 1}$ and $∣ Q_{a} ∣ < ∣ Q_{a + 1} ∣$ . For a poset $Q$ , let $C_{t} (Q)$ denote the set of…

math.CO2026

Ramsey-TurÃ¡n theory for partially-ordered sets

Gyula O. H. Katona, Yaping Mao

We introduce weak and strong poset Ramsey-TurÃ¡n numbers for $t$ -chains in host poset families, focusing on the Boolean lattice family $B = {B_{n} : n \geq 1}$ . For any poset $…

math.CO2026

Intersecting families with bounded intersections

Kristina Ago, Gyula O. H. Katona

Let $F \subset 2^{[n]}$ be an $s$ -uniform family such that every two distinct sets have a nonempty intersection but intersect in at most $k$ elements. By the well-known Ray…

math.CO2026

ErdÅs-GyÃ¡rfÃ¡s problem for partially ordered sets

Gyula O. H. Katona, Yaping Mao

Given integers $p, q, t$ with $1 \leq t \leq p$ and $1 \leq q \leq h_{p} (t)$ , a strong $(p, q, t)$ -coloring of the Boolean lattice $B_{n}$ is a coloring of its $t$ -chains such that every induc…

math.CO2026

Most probably trangle-free graphs

Yuhang Bai, Gyula O. H. Katona, Zixuan Yang

The celebrated Mantel's theorem states that any triangle-free graph on $n$ vertices contains at most $⌊ n^{2} /4 ⌋$ edges. It is natural to ask how many triangle…

math.CO2026

Boolean lattice without small rainbow subposets

Gyula O. H. Katona, Yaping Mao, Kenta Ozeki +2

A Boolean lattice $B_{n} = (2^{X}, \leq)$ is the power set of an $n$ -element ground set $X$ equipped with inclusion relation. For two posets $P$ and $Q$ , we…

Multiplicity for partially ordered sets

Ramsey-TurÃ¡n theory for partially-ordered sets

Intersecting families with bounded intersections

ErdÅs-GyÃ¡rfÃ¡s problem for partially ordered sets

Most probably trangle-free graphs

Boolean lattice without small rainbow subposets

ErdÅs-GyÃ¡rfÃ¡s problem for partially ordered sets