Peter Frankl

activity

20242026

most citedOn the product of cross-intersecting families with maximal covering number

2 citations · 2 across the 2 of their papers we have counts for

collaborators

6 papers

math.CO2026★ 2 cited

On the product of cross-intersecting families with maximal covering number

Long Lin, Peter Frankl, Hehui Wu

For integers $k, ℓ \geq 2$ let $m (k, ℓ)$ denote the maximum of $∣ F ∣∣ G ∣$ where the maximum is taken over all pairs of cross-intersecting families, $\mathca…

math.CO2026

On the product of cross-intersecting families with small covering number

Peter Frankl, Long Lin, Hehui Wu

A central problem in extremal set theory is to determine or estimate $m (n, k, t), n > 2 k \geq 2 t$ , the maximum size of an intersecting $k$ -graph and covering number at least $t$ (see the…

math.CO2026

Matching and intersection problems for non-trivial $r$ -partite $r$ -uniform hypergraphs

Peter Frankl, Jiaxi Nie

A central theme in extremal combinatorics is the study of the maximum number of edges in an $r$ -uniform hypergraph ( $r$ -graph) with matching number at most $s$ (the ErdÅs Matching…

math.CO2025

Intersecting Families of Spanning Trees

Peter Frankl, Glenn Hurlbert, Ferdinand Ihringer +4

A family $F$ of spanning trees of the complete graph on $n$ vertices $K_{n}$ is \emph{ $t$ -intersecting} if any two members have a forest on $t$ edges in common. We prove an…

math.CO2025

The Hajnal--Rothschild problem

Peter Frankl, Andrey Kupavskii

For a family $F$ define $I^½ (F, t)$ as the largest $s$ for which there exist $A_{1}, \dots, A_{s} \in F$ such that for $i \neq = j$ we have $∣ A_{i} \cap A_{j} ∣ < t$ . Wh…

math.CO2024

Non-trivial $r$ -wise agreeing families