Journal ArticleDOI
The Erdős Matching Conjecture and concentration inequalities
Peter Frankl,Andrey Kupavskii +1 more
TLDR
In this paper , it was shown that |F| ≥ (nk)−(n−sk), provided n≥53sk−23s and s is sufficiently large.About:
This article is published in Journal of Combinatorial Theory, Series B.The article was published on 2022-11-01. It has received 36 citations till now. The article focuses on the topics: Computer science & Disjoint sets.read more
Citations
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Sharp bounds for the chromatic number of random Kneser graphs
Sergei Kiselev,Andrey Kupavskii +1 more
TL;DR: The chromatic number of the random Kneser graph with edges connecting pairs of disjoint sets was shown to be n-2k+2-2l in this paper.
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Dirac-type theorems in random hypergraphs
Asaf Ferber,Matthew Kwan +1 more
TL;DR: In this article, the absorbing method was used to prove that a random k-uniform hypergraph with n vertices and edge probability at least (1 + ε + varepsilon)m{d}(k,n)p has a perfect matching.
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On the rainbow matching conjecture for 3-uniform hypergraphs
TL;DR: In this paper, Huang, Loh, and Sudakov showed that the rainbow version of Erdős matching conjecture holds for 3-uniform hypergraphs, which can be viewed as a stability version of a result of Łuczak and Mieczkowska.
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Rainbow matchings for 3-uniform hypergraphs
TL;DR: This paper shows that for $n\in 3\mathbb{Z}$ sufficiently large, if $F_1, \ldots, F_{n/3}$ are 3-uniform hypergrapghs with a common vertex set and $\delta_1(F_i)>{n-1\choose 2}-{2 n/3\choosen 2}$ for $i\in [n/ 3]$, then $H
Journal ArticleDOI
Old and new applications of Katona’s circle
TL;DR: The present paper is to honour Gyula Katona, my teacher on the occasion of his 80th birthday, with new proofs of old results and the solution for the Katona Circle of some notoriously difficult problems.
References
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Journal ArticleDOI
On the Shannon capacity of a graph
TL;DR: It is proved that the Shannon zero-error capacity of the pentagon is \sqrt{5} and a well-characterized, and in a sense easily computable, function is introduced which bounds the capacity from above and equals the capacity in a large number of cases.
Journal ArticleDOI
Intersection theorems for systems of finite sets
Paul Erdös,Chao Ko,Richard Rado +2 more
TL;DR: In this article, the obliteration operator is used to remove from any system of elements the element above which it is placed, and the set of all systems (ao,av...,dn) such that avc[0,m); \av\ 1 (v < »),
Journal ArticleDOI
Weighted sums of certain dependent random variables
TL;DR: In this paper, a sequence of bounded martingale differences on a probability space is shown to be bounded almost surely (a.s.) for n = 1, 2, etc.
Book ChapterDOI
Probability Inequalities for Sums of Bounded Random Variables
N. I. Fisher,Pranab Kumar Sen +1 more
TL;DR: In this article, the Bienayme-Chebyshev inequality for random variables with finite rnean and variance was shown to hold for n independent, identically distributed random variables.