22 citations · 53 across the 17 of their papers we have counts for
21 papers
Induced poset saturation in the hypergrid
R. Altar Ciceksiz, Victor Falgas-Ravry, Sabrina Lato +1
Set . The hypergrid is the collection of functions . We equip it with the natural partial order by letting when…
On density conditions for transversal trees in multipartite graphs
Leila Badakhshian, Victor Falgas-Ravry, Maryam Sharifzadeh
Let be an -partite graph such that the edge density between any two parts is at least . How large does need to be to guarantee that contains a connected transvers…
The induced saturation problem for posets
Andrea Freschi, Simón Piga, Maryam Sharifzadeh +1
For a fixed poset , a family of subsets of is induced -saturated if does not contain an induced copy of , but for every subset of …
Geometric constructions for Ramsey-Turán theory
Hong Liu, Christian Reiher, Maryam Sharifzadeh +1
Combining two classical notions in extremal combinatorics, the study of Ramsey-Turán theory seeks to determine, for integers and , the number $\mathsf{RT}_p(n,K_…
Stability from graph symmetrisation arguments with applications to inducibility
Hong Liu, Oleg Pikhurko, Maryam Sharifzadeh +1
We present a sufficient condition for the stability property of extremal graph problems that can be solved via Zykov's symmetrisation. Our criterion is stated in terms of an analyt…
Limits of Latin squares
Frederik Garbe, Robert Hancock, Jan Hladký +1
We develop a limit theory of Latin squares, paralleling the recent limit theories of dense graphs and permutations. We introduce a notion of density, an appropriate version of the…
Characterization of quasirandom permutations by a pattern sum
Timothy F. N. Chan, Daniel Kral, Jonathan A. Noel +3
It is known that a sequence Pi_i of permutations is quasirandom if and only if the pattern density of every 4-point permutation in Pi_i converges to 1/24. We show that there is a s…
Asymptotic Structure for the Clique Density Theorem
Jaehoon Kim, Hong Liu, Oleg Pikhurko +1
The famous Erdős-Rademacher problem asks for the smallest number of -cliques in a graph with the given number of vertices and edges. Despite decades of active attempts, the asym…
Groups with few maximal sum-free sets
Hong Liu, Maryam Sharifzadeh
We show that, in contrast to the integers setting, almost all even order abelian groups have exponentially fewer maximal sum-free sets than , where denotes t…
Structure and Supersaturation for Intersecting Families
József Balogh, Shagnik Das, Hong Liu +2
The extremal problems regarding the maximum possible size of intersecting families of various combinatorial objects have been extensively studied. In this paper, we investigate sup…
On the maximum number of integer colourings with forbidden monochromatic sums
Hong Liu, Maryam Sharifzadeh, Katherine Staden
Let denote the maximum number of colourings of with colours such that each colour class is sum-free. Here, a sum is a subset $\…
Edges not in any monochromatic copy of a fixed graph
Hong Liu, Oleg Pikhurko, Maryam Sharifzadeh
For a sequence of graphs, let denote the maximum number of edges not contained in any monochromatic copy of in colour , f…
Proof of Komlós's conjecture on Hamiltonian subsets
Jaehoon Kim, Hong Liu, Maryam Sharifzadeh +1
Komlós conjectured in 1981 that among all graphs with minimum degree at least , the complete graph minimises the number of Hamiltonian subsets, where a subset of verti…
Local conditions for exponentially many subdivisions
Hong Liu, Maryam Sharifzadeh, Katherine Staden
Given a graph , let be the number of subdivisions of , each with a different vertex set, which one can guarantee in a graph in which every edge lies in at least…
On two problems in Ramsey-Turán theory
József Balogh, Hong Liu, Maryam Sharifzadeh
Alon, Balogh, Keevash and Sudakov proved that the -partite Turán graph maximizes the number of distinct -edge-colorings with no monochromatic for all fixed and…
The number of subsets of integers with no -term arithmetic progression
József Balogh, Hong Liu, Maryam Sharifzadeh
Addressing a question of Cameron and Erd\Ho s, we show that, for infinitely many values of , the number of subsets of that do not contain a -term arithmet…
Sharp bound on the number of maximal sum-free subsets of integers
József Balogh, Hong Liu, Maryam Sharifzadeh +1
Cameron and Erdős asked whether the number of \emph{maximal} sum-free sets in is much smaller than the number of sum-free sets. In the same paper they gave a low…
The typical structure of maximal triangle-free graphs
József Balogh, Hong Liu, Šárka Petříčková +1
Recently, settling a question of Erdős, Balogh and Petříčková showed that there are at most -vertex maximal triangle-free graphs, matching the previously know…
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…
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…