P. Frankl

activity

20242026

collaborators

11 papers

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

One of the central problems in extremal set theory is the determination of the maximum size of an $r$ -wise $t$ -intersecting $k$ -graph on $n$ vertices. For $r = 2$ after decades of ef…

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…

math.CO2024

The maximum sturdiness of intersecting families

Peter Frankl, Jian Wang

Given a family $F \subset 2^{[n]}$ and $1 \leq i \neq = j \leq n$ , we use $F (i ˉ, j)$ to denote the family $\{F\setminus \{j\}\colon F\in \mathcal{F},\ F\cap \{i,j…

math.CO2024

On the Matching Problem in Random Hypergraphs

Peter Frankl, Jiaxi Nie, Jian Wang

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

math.CO2024

On $r$ -wise $t$ -intersecting uniform families

Peter Frankl, Jian Wang

We consider families, $F$ of $k$ -subsets of an $n$ -set. For integers $r \geq 2$ , $t \geq 1$ , $F$ is called $r$ -wise $t$ -intersecting if any $r$ of its members hav…

math.CO2024

On odd covers of cliques and disjoint unions

Calum Buchanan, Alexander Clifton, Eric Culver +5

Babai and Frankl posed the ``odd cover problem" of finding the minimum cardinality of a collection of complete bipartite graphs such that every edge of the complete graph of order…

math.CO2024

Intersecting families with large shadow degree

Peter Frankl, Jian Wang

A $k$ -uniform family $F$ is called intersecting if $F \cap F^{'} \neq = \emptyset$ for all $F, F^{'} \in F$ . The shadow family $\partial F$ is the family of $(k-1…

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 maximum sturdiness of intersecting families

On the Matching Problem in Random Hypergraphs

On r-wise t-intersecting uniform families

On odd covers of cliques and disjoint unions

Intersecting families with large shadow degree

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

On $r$ -wise $t$ -intersecting uniform families