P. Frankl

activity

20112026

s

pairwise disjoint sets

15 citations · 86 across the 50 of their papers we have counts for

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11 papers · 1 filter

math.CO2022★ 3 cited

Best possible bounds on the double-diversity of intersecting hypergraphs

Peter Frankl, Jian Wang

For a family $F \subset (k [ n ])$ and two elements $x, y \in [n]$ define $F (x ˉ, y ˉ) = {F \in F : x \in / F, y \in / F}$ . The double-di…

math.CO2022★ 1 cited

Turán graphs with bounded matching number

Noga Alon, Peter Frankl

We determine the maximum possible number of edges of a graph with $n$ vertices, matching number at most $s$ and clique number at most $k$ for all admissible values of the parameter…

math.CO2022

Improved bounds concerning the maximum degree of intersecting hypergraphs

Peter Frankl, Jian Wang

For positive integers $n > k > t$ let $(k [ n ])$ denote the collection of all $k$ -subsets of the standard $n$ -element set $[n] = {1, \dots, n}$ . Subsets of $(k [ n ])$ are ca…

math.CO2022

On the maximum of the sum of the sizes of non-trivial cross-intersecting families

Peter Frankl

We consider families of k-subsets of the standard n-set. Two families F, G are said to be cross-intersecting if every member of F has non-empty intersection with every member of G.…

math.CO2022★ 1 cited

Intersecting families with covering number three

Peter Frankl, Jian Wang

We consider $k$ -graphs on $n$ vertices, that is, $F \subset (k [ n ])$ . A $k$ -graph $F$ is called intersecting if $F \cap F^{'} \neq = \emptyset$ for all $F,F'\in…

math.CO2022

A Product Version of the Hilton-Milner Theorem

Peter Frankl, Jian Wang

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