P. Frankl

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20112026

s

pairwise disjoint sets

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

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Showing 2020Show all

10 papers · 1 filter

math.CO2020

On the Maximum Number of Edges in Hypergraphs with Fixed Matching and Clique Number

Peter Frankl, Erica L. L. Liu, Jian Wang

For a $k$ -graph $F \subset (k [ n ])$ , the clique number of $F$ is defined to be the maximum size of a subset $Q$ of $[n]$ with $\binom{Q}{k}\subset \mathca…

math.CO2020

Old and new applications of Katona's circle

Peter Frankl

Several new applications of Katona's circle are given.

math.CO2020★ 1 cited

On non-empty cross-intersecting families

Chao Shi, Peter Frankl, Jianguo Qian

Let $2^{[n]}$ and $(i [ n ])$ be the power set and the class of all $i$ -subsets of ${1, 2, \dots, n}$ , respectively. We call two families $A$ and $B$ cross…

math.CO2020

Intersection theorems for triangles

Peter Frankl, Andreas Holmsen, Andrey Kupavskii

Given a family of sets on the plane, we say that the family is intersecting if for any two sets from the family their interiors intersect. In this paper, we study intersecting fami…

math.CO2020

Analogues of Katona's and Milner's Theorems for two families

Peter Frankl, Willie Wong H. W

Let $n > s > 0$ be integers, $X$ an $n$ -element set and $A, B \subset 2^{X}$ two families. If $∣ A \cup B ∣ \leq s$ for all $A \in A, B \in B$ , then $\math…

math.CO2020

Shattered matchings in intersecting hypergraphs

Peter Frankl, Janos Pach

Let $X$ be an $n$ -element set, where $n$ is even. We refute a conjecture of J. Gordon and Y. Teplitskaya, according to which, for every maximal intersecting family $F$ of…