Zobrazeno 1 - 10
of 288
pro vyhledávání: '"Patkós, Balázs"'
Autor:
Martin, Ryan R., Patkós, Balázs
A classical result of Kleitman determines the maximum number $f(n,s)$ of subsets in a family $\mathcal{F}\subseteq 2^{[n]}$ of sets that do not contain distinct sets $F_1,F_2,\dots,F_s$ that are pairwise disjoint in the case $n\equiv 0,-1$ (mod $s$).
Externí odkaz:
http://arxiv.org/abs/2409.08694
Autor:
Martin, Ryan R., Patkós, Balázs
The Erd\H os Matching Conjecture states that the maximum size $f(n,k,s)$ of a family $\mathcal{F}\subseteq \binom{[n]}{k}$ that does not contain $s$ pairwise disjoint sets is $\max\{|\mathcal{A}_{k,s}|,|\mathcal{B}_{n,k,s}|\}$, where $\mathcal{A}_{k,
Externí odkaz:
http://arxiv.org/abs/2404.12971
We study the following game version of the generalized graph Tur\'an problem. For two fixed graphs F and H, two players, Max and Mini, alternately claim unclaimed edges of the complete graph Kn such that the graph G of the claimed edges must remain F
Externí odkaz:
http://arxiv.org/abs/2404.02288
Autor:
Gerbner, Dániel, Patkós, Balázs
The Kneser cube $Kn_n$ has vertex set $2^{[n]}$ and two vertices $F,F'$ are joined by an edge if and only if $F\cap F'=\emptyset$. For a fixed graph $G$, we are interested in the most number $vex(n,G)$ of vertices of $Kn_n$ that span a $G$-free subgr
Externí odkaz:
http://arxiv.org/abs/2402.02525
In this paper, we address problems related to parameters concerning edge mappings of graphs. Inspired by Ramsey's Theorem, the quantity $m(G, H)$ is defined to be the minimum number $n$ such that for every $f: E(K_n) \rightarrow E(K_n)$ either there
Externí odkaz:
http://arxiv.org/abs/2402.01004
In this paper, we address problems related to parameters concerning edge mappings of graphs. The quantity $h(n,G)$ is defined to be the maximum number of edges in an $n$-vertex graph $H$ such that there exists a mapping $f: E(H)\rightarrow E(H)$ with
Externí odkaz:
http://arxiv.org/abs/2402.01006
Publikováno v:
Applicable Analysis and Discrete Mathematics, 2024 Apr 01. 18(1), 193-214.
Externí odkaz:
https://www.jstor.org/stable/27303532
Autor:
Gerbner, Dániel, Keszegh, Balázs, Nagy, Dániel T., Nagy, Kartal, Pálvölgyi, Dömötör, Patkós, Balázs, Wiener, Gábor
We study the query complexity on slices of Boolean functions. Among other results we show that there exists a Boolean function for which we need to query all but 7 input bits to compute its value, even if we know beforehand that the number of 0's and
Externí odkaz:
http://arxiv.org/abs/2309.13678
Autor:
Patkós, Balázs, Treglown, Andrew
Given two posets $P,Q$ we say that $Q$ is $P$-free if $Q$ does not contain a copy of $P$. The size of the largest $P$-free family in $2^{[n]}$, denoted by $La(n,P)$, has been extensively studied since the 1980s. We consider several related problems.
Externí odkaz:
http://arxiv.org/abs/2308.14863
Autor:
Pálvölgyi, Dömötör, Patkós, Balázs
We introduce two variants of the poset saturation problem. For a poset $P$ and the Boolean lattice $\mathcal{B}_n$, a family $\mathcal{F}$ of sets, not necessarily from $\mathcal{B}_n$, is \textit{projective $P$-saturated} if (i) it does not contain
Externí odkaz:
http://arxiv.org/abs/2306.10387