105 citations · 718 across the 103 of their papers we have counts for
9 papers · 2 filters
Maximum density of an induced 5-cycle is achieved by an iterated blow-up of a 5-cycle
József Balogh, Ping Hu, Bernard Lidický +1
Let denote the maximum number of induced copies of 5-cycles in graphs on vertices. For large enough, we show that $C(n)=a\cdot b\cdot c \cdot d \cdot e + C(a)+C(b)+C…
Minimum number of monotone subsequences of length 4 in permutations
József Balogh, Ping Hu, Bernard Lidický +3
We show that for every sufficiently large , the number of monotone subsequences of length four in a permutation on points is at least $\binom{\lfloor n/3 \rfloor}{4} + \bino…
The number of the maximal triangle-free graphs
József Balogh, Šárka Petříčková
Paul Erdős suggested the following problem: Determine or estimate the number of maximal triangle-free graphs on vertices. Here we show that the number of maximal triangle-free…
The number of maximal sum-free subsets of integers
József Balogh, Hong Liu, Maryam Sharifzadeh +1
Cameron and Erdős raised the question of how many maximal sum-free sets there are in , giving a lower bound of . In this paper we prove…
Rainbow triangles in three-colored graphs
Jozsef Balogh, Ping Hu, Bernard Lidicky +3
Erdos and Sos proposed a problem of determining the maximum number F(n) of rainbow triangles in 3-edge-colored complete graphs on n vertices. They conjectured that F(n) = F(a)+ F(b…
Intersecting families of discrete structures are typically trivial
József Balogh, Shagnik Das, Michelle Delcourt +2
The study of intersecting structures is central to extremal combinatorics. A family of permutations is \emph{-intersecting} if any two permutations in…
The typical structure of graphs with no large cliques
József Balogh, Neal Bushaw, Maurício Collares Neto +3
In 1987, Kolaitis, Prömel and Rothschild proved that, for every fixed , almost every -vertex -free graph is -partite. In this paper we extend this…
A random version of Sperner's theorem
József Balogh, Richard Mycroft, Andrew Treglown
Let denote the power set of , ordered by inclusion, and let be obtained from by selecting elements from i…
Transitive Triangle Tilings in Oriented Graphs
József Balogh, Allan Lo, Theodore Molla
In this paper, we prove an analogue of Corrádi and Hajnal's classical theorem. There exists such that for every when the following holds. If $…