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pro vyhledávání: '"Frankl, Peter"'
We study a variant of the Erd\H{o}s Matching Problem in random hypergraphs. Let $\mathcal{K}_p(n,k)$ denote the Erd\H{o}s-R\'enyi random $k$-uniform hypergraph on $n$ vertices where each possible edge is included with probability $p$. We show that wh
Externí odkaz:
http://arxiv.org/abs/2410.15585
Autor:
Frankl, Peter, Wang, Jian
We consider families, $\mathcal{F}$ of $k$-subsets of an $n$-set. For integers $r\geq 2$, $t\geq 1$, $\mathcal{F}$ is called $r$-wise $t$-intersecting if any $r$ of its members have at least $t$ elements in common. The most natural construction of su
Externí odkaz:
http://arxiv.org/abs/2409.19344
Autor:
Buchanan, Calum, Clifton, Alexander, Culver, Eric, Frankl, Péter, Nie, Jiaxi, Ozeki, Kenta, Rombach, Puck, Yin, Mei
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 $n$ is covered an odd number of times. In a previous paper with O'Neil
Externí odkaz:
http://arxiv.org/abs/2408.08598
Autor:
Frankl, Peter, Kupavskii, Andrey
Let us consider a collection $\mathcal G$ of codewords of length $n$ over an alphabet of size $s$. Let $t_1,\ldots, t_s$ be nonnegative integers. What is the maximum of $|\mathcal G|$ subject to the condition that any two codewords should have at lea
Externí odkaz:
http://arxiv.org/abs/2408.08221
Autor:
Frankl, Peter, Wang, Jian
A $k$-uniform family $\mathcal{F}$ is called intersecting if $F\cap F'\neq \emptyset$ for all $F,F'\in \mathcal{F}$. The shadow family $\partial \mathcal{F}$ is the family of $(k-1)$-element sets that are contained in some members of $\mathcal{F}$. T
Externí odkaz:
http://arxiv.org/abs/2406.00465
There are four non-isomorphic configurations of triples that can form a triangle in a $3$-uniform hypergraph. Forbidding different combinations of these four configurations, fifteen extremal problems can be defined, several of which already appeared
Externí odkaz:
http://arxiv.org/abs/2405.16452
Autor:
Frankl, Peter, Kupavskii, Andrey
A family of sets is $r$-wise agreeing if for any $r$ sets from the family there is an element $x$ that is either contained in all or contained in none of the $r$ sets. The study of such families is motivated by questions in discrete optimization. In
Externí odkaz:
http://arxiv.org/abs/2404.14178
Extending the notion of sunflowers, we call a family of at least two sets an odd-sunflower if every element of the underlying set is contained in an odd number of sets or in none of them. It follows from the Erd\H os--Szemer\'edi conjecture, recently
Externí odkaz:
http://arxiv.org/abs/2310.16701
Autor:
Frankl, Peter, Wang, Jian
Let $\mathcal{F}\subset \binom{X}{k}$ be a family consisting of $k$-subsets of the $n$-set $X$. Suppose that $\mathcal{F}$ is intersecting, i.e., $F\cap F'\neq \emptyset$ for all $F,F'\in \mathcal{F}$. Let $\Delta(\mathcal{F})$ be the maximum degree
Externí odkaz:
http://arxiv.org/abs/2308.14028
Autor:
Hegedüs, Gábor, Frankl, Péter
Let $X$ be an $n$-element set. A set-pair system $\mbox{$\cal P$}=\{(A_i,B_i)\}_{1\leq i\leq m}$ is a collection of pairs of disjoint subsets of $X$. It is called skew Bollob\'as system if $A_i\cap B_j\neq \emptyset$ for all $1\leq i
Externí odkaz:
http://arxiv.org/abs/2307.14704