P. Frankl

activity

20242026

collaborators

8 papers

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 ErdÅs-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

On the Matching Problem in Random Hypergraphs

Peter Frankl, Jiaxi Nie, Jian Wang

We study a variant of the ErdÅs Matching Problem in random hypergraphs. Let $K_{p} (n, k)$ denote the ErdÅs-RÃ©nyi random $k$ -uniform hypergraph on $n$ vertices where each…

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…

A product version of the Hilton-Milner Theorem II

The Exact ErdÅs-Ko-Rado Theorem for 3-wise t-intersecting uniform families

On the largest degrees in intersecting hypergraphs

On the Matching Problem in Random Hypergraphs

The overflow in the Katona Theorem

On resilient hypergraphs

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