P. Frankl

activity

20242026

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11 papers · 1 filter

math.CO2026

Stability for Helly-type and triangle-free families

Peter Frankl, Jian Wang

We consider $k$ -graphs, $F \subset (k [ n ])$ , $k \geq 3$ . A $k$ -graph is called intersecting if any two of its edges have non-empty intersection. It is called a star…

math.CO2026

A product version of the Hilton-Milner Theorem II

Peter Frankl, Jian Wang

Two families $F, G$ of $k$ -subsets of ${1, 2, \dots, n}$ are called {\it non-trivial cross-intersecting} if $F \cap G \neq = \emptyset$ for all $F\in \mathcal{F}, G\…

math.CO2026

The Exact Erdős-Ko-Rado Theorem for 3-wise $t$ -intersecting uniform families

Peter Frankl, Jian Wang

Let $F$ be a family of $k$ -element subsets of ${1, 2, \dots, n}$ . For $t \geq 1$ , we say that $F$ is {\it 3-wise $t$ -intersecting} if $|F_1\cap F_2\cap F_3|\geq…

math.CO2025

On the largest degrees in intersecting hypergraphs

Peter Frankl, Jian Wang

Let $(k [ n ])$ denote the collection of all $k$ -subsets of the standard $n$ -set $[n] = {1, 2, \dots, n}$ . Let $n > 2 k$ and let $F \subset (k [ n ])$ be an {\it inte…

math.CO2025

The overflow in the Katona Theorem

Peter Frankl, Jian Wang

Let $n > 2 r > 0$ be integers. We consider families $F$ of subsets of an $n$ -element set, in which the union of any two members has size at most $2 r$ . One of our results state…

math.CO2025

On resilient hypergraphs

Peter Frankl, Jian Wang

The matching number of a $k$ -graph is the maximum number of pairwise disjoint edges in it. The $k$ -graph is called $t$ -resilient if omitting $t$ vertices never decreases its matchi…

Stability for Helly-type and triangle-free families

A product version of the Hilton-Milner Theorem II

The Exact Erdős-Ko-Rado Theorem for 3-wise t-intersecting uniform families

On the largest degrees in intersecting hypergraphs

The overflow in the Katona Theorem

On resilient hypergraphs

The Exact Erdős-Ko-Rado Theorem for 3-wise $t$ -intersecting uniform families