P. Frankl

activity

20242026

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5 papers · 1 filter

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…

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

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