Zobrazeno 1 - 10
of 497
pro vyhledávání: '"Béla Bollobás"'
Publikováno v:
Forum of Mathematics, Sigma, Vol 3 (2015)
For natural numbers $n,r\in \mathbb{N}$ with $n\geqslant r$, the Kneser graph $K(n,r)$ is the graph on the family of $r$-element subsets of $\{1,\ldots ,n\}$ in which two sets are adjacent if and only if they are disjoint. Delete the edges of $K(n,r)
Externí odkaz:
https://doaj.org/article/c66cc5f41008466b81d9f826dbc6fb81
In its usual form, Freiman's 3 k − 4 $3k-4$ theorem states that if A $A$ and B $B$ are subsets of Z ${\mathbb {Z}}$ of size k $k$ with small sumset (of size close to 2 k $2k$ ), then they are very close to arithmetic progressions. Our aim in this p
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ed983e9d95ed27e9a37b87d870870fba
https://www.repository.cam.ac.uk/handle/1810/350321
https://www.repository.cam.ac.uk/handle/1810/350321
Publikováno v:
Inventiones mathematicae. 228:377-414
Since their introduction by Erdős in 1950, covering systems (that is, finite collections of arithmetic progressions that cover the integers) have been extensively studied, and numerous questions and conjectures have been posed regarding the existenc
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::307813746ef90af36b4edb157f34ef69
https://doi.org/10.1007/s00222-021-01087-5
https://doi.org/10.1007/s00222-021-01087-5
Publikováno v:
Algebra & Number Theory. 15:609-626
A covering system is a finite collection of arithmetic progressions whose union is the set of integers. The study of covering systems with distinct moduli was initiated by Erd\H{o}s in 1950, and over the following decades numerous problems were posed
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::29824fa894f5181d68eff027920773b9
https://doi.org/10.2140/ant.2021.15.609
https://doi.org/10.2140/ant.2021.15.609
Autor:
Béla Bollobás
Publikováno v:
Journal de théorie des nombres de Bordeaux. 34:515-516
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::0dda7eb791b2a68cac0ecba2151591c7
https://doi.org/10.5802/jtnb.1212
https://doi.org/10.5802/jtnb.1212
Autor:
Béla Bollobás
Lovers of mathematics, young and old, professional and amateur, will enjoy this book. It is mathematics with fun: a collection of attractive problems that will delight and test readers. Many of the problems are drawn from the large number that have e
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::4bb83f55e9ef3cc38b8b6e3578002d9a
https://doi.org/10.1017/9781108973885
https://doi.org/10.1017/9781108973885
Autor:
Béla Bollobás, Oliver Riordan
Publikováno v:
Handbook of the Tutte Polynomial and Related Topics ISBN: 9780429161612
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::940b4734557eb02cf9a1e7fb5e5e98ab
https://doi.org/10.1201/9780429161612-3
https://doi.org/10.1201/9780429161612-3
Publikováno v:
Acta Mathematica Hungarica. 161:540-549
A covering system is a finite collection of arithmetic progressions whose union is the set of integers. The study of these objects was initiated by Erdős in 1950, and over the following decades he asked many questions about them. Most famously, he a
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::54eaded90fb322b6a0af61976496e9b8
https://doi.org/10.1007/s10474-020-01048-z
https://doi.org/10.1007/s10474-020-01048-z
Publikováno v:
Acta Mathematica Hungarica. 161:197-200
In this short note we give a simple proof of a 1962 conjecture of Erdős, first proved in 1969 by Crittenden and Vanden Eynden, and note two corollaries.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::c38379e25284b52088b3317aa70ffd93
https://doi.org/10.1007/s10474-019-00980-z
https://doi.org/10.1007/s10474-019-00980-z
Publikováno v:
Discrete Applied Mathematics. 260:66-74
For a constant γ ∈ [ 0 , 1 ] and a graph G , let ω γ ( G ) be the largest integer k for which there exists a k -vertex subgraph of G with at least γ k 2 edges. We show that if 0 p γ 1 then ω γ ( G n , p ) is concentrated on a set of two inte
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::94d58b855527f43bf1c430351bcf61dd
https://doi.org/10.1016/j.dam.2019.01.032
https://doi.org/10.1016/j.dam.2019.01.032