194 citations · 2.2k across the 69 of their papers we have counts for
31 papers · 1 filter
A Turán-type theorem for large-distance graphs in Euclidean spaces, and related isodiametric problems
Martin Doležal, Jan Hladký, Jan Kolář +3
Given a measurable set we consider the "large-distance graph" , on the ground set , in which each pair of points from whose distance is…
A limit theorem for small cliques in inhomogeneous random graphs
Jan Hladky, Christos Pelekis, Matas Sileikis
The theory of graphons comes with a natural sampling procedure, which results in an inhomogeneous variant of the Erdős--Rényi random graph, called -random graphs. We prove, via…
Cut-norm and entropy minimization over weak* limits
Martin Dolezal, Jan Hladky
We prove that the accumulation points of a sequence of graphs with respect to the cut-distance are exactly the weak limit points of subsequences of the adj…
Almost all trees are almost graceful
Anna Adamaszek, Peter Allen, Codrut Grosu +1
The Graceful Tree Conjecture of Rosa from 1967 asserts that the vertices of each tree T of order n can be injectively labelled by using the numbers {1,2,...,n} in such a way that t…
Komlós's tiling theorem via graphon covers
Jan Hladký, Ping Hu, Diana Piguet
Komlos [Komlos: Tiling Turan Theorems, Combinatorica, 2000] determined the asymptotically optimal minimum-degree condition for covering a given proportion of vertices of a host gra…
Matching polytons
Martin Dolezal, Jan Hladky
Hladky, Hu, and Piguet [Tilings in graphons, preprint] introduced the notions of matching and fractional vertex covers in graphons. These are counterparts to the corresponding noti…
Tilings in graphons
Jan Hladky, Ping Hu, Diana Piguet
We introduce a counterpart to the notion of vertex disjoint tilings by copy of a fixed graph F to the setting of graphons. The case F=K_2 gives the notion of matchings in graphons.…
Chromatic roots and limits of dense graphs
Peter Csikvari, Peter E. Frenkel, Jan Hladky +1
In this short note we observe that recent results of Abert and Hubai and of Csikvari and Frenkel about Benjamini--Schramm continuity of the holomorphic moments of the roots of the…
Cliques in dense inhomogeneous random graphs
Martin Doležal, Jan Hladký, András Máthé
The theory of dense graph limits comes with a natural sampling process which yields an inhomogeneous variant G(n,W) of the Erdos-Renyi random graph. Here we study the clique number…
The approximate Loebl-Komlós-Sós Conjecture II: The rough structure of LKS graphs
Jan Hladký, János Komlós, Diana Piguet +3
This is the second of a series of four papers in which we prove the following relaxation of the Loebl-Komlos--Sos Conjecture: For every there exists a number such that…
The approximate Loebl-Komlós-Sós Conjecture IV: Embedding techniques and the proof of the main result
Jan Hladký, János Komlós, Diana Piguet +3
This is the last paper of a series of four papers in which we prove the following relaxation of the Loebl-Komlos-Sos Conjecture: For every there exists a number~ such th…
The Approximate Loebl-Komlós-Sós Conjecture III: The finer structure of LKS graphs
Jan Hladký, János Komlós, Diana Piguet +3
This is the third of a series of four papers in which we prove the following relaxation of the Loebl-Komlos-Sos Conjecture: For every there exists a number such that fo…
The approximate Loebl-Komlós-Sós Conjecture I: The sparse decomposition
Jan Hladký, János Komlós, Diana Piguet +3
In a series of four papers we prove the following relaxation of the Loebl-Komlos-Sos Conjecture: For every there exists a number such that for every every -v…
The approximate Loebl-Komlos-Sos conjecture and embedding trees in sparse graphs
Jan Hladky, Diana Piguet, Miklos Simonovits +2
Loebl, Komlós and Sós conjectured that every -vertex graph with at least vertices of degree at least contains each tree of order as a subgraph. We give a…
An approximate version of the Tree Packing Conjecture
Julia Böttcher, Jan Hladký, Diana Piguet +1
We prove that for any pair of constants and and for sufficiently large, every family of trees of orders at most , maximum degrees at most , and with at most $\b…
A density Corrádi-Hajnal Theorem
Peter Allen, Julia Böttcher, Jan Hladký +1
We find, for all sufficiently large and each , the maximum number of edges in an -vertex graph which does not contain vertex-disjoint triangles. This extends a resu…
An extension of Turán's Theorem, uniqueness and stability
Peter Allen, Julia Böttcher, Jan Hladký +1
We determine the maximum number of edges of an -vertex graph with the property that none of its -cliques intersects a fixed set . For , the…
Poset limits can be totally ordered
Jan Hladky, Andras Mathe, Viresh Patel +1
S.Janson [Poset limits and exchangeable random posets, Combinatorica 31 (2011), 529--563] defined limits of finite posets in parallel to the emerging theory of limits of dense grap…
Dense flag triangulations of 3-manifolds via extremal graph theory
Michal Adamaszek, Jan Hladky
We characterize f-vectors of sufficiently large three-dimensional flag Gorenstein* complexes, essentially confirming a conjecture of Gal [Discrete Comput. Geom., 34 (2), 269--284,…
Non-three-colorable common graphs exist
Hamed Hatami, Jan Hladky, Daniel Kral +2
A graph H is called common if the total number of copies of H in every graph and its complement asymptotically minimizes for random graphs. A former conjecture of Burr and Rosta, e…
On the Number of Pentagons in Triangle-Free Graphs
Hamed Hatami, Jan Hladký, Daniel Král +2
Using the formalism of flag algebras, we prove that every triangle-free graph with vertices contains at most cycles of length five. Moreover, the equality is atta…
Turánnical hypergraphs
Peter Allen, Julia Böttcher, Jan Hladký +1
This paper is motivated by the question of how global and dense restriction sets in results from extremal combinatorics can be replaced by less global and sparser ones. The result…
Hamilton cycles in dense vertex-transitive graphs
Demetres Christofides, Jan Hladký, András Máthé
A famous conjecture of Lovász states that every connected vertex-transitive graph contains a Hamilton path. In this article we confirm the conjecture in the case that the graph is…
The extremal function for partial bipartite tilings
Codrut Grosu, Jan Hladky
For a fixed bipartite graph H and given number c, 0<c<1, we determine the threshold T_H(c) which guarantees that any n-vertex graph with at edge density at least T_H(c) contains $(…