4 citations · 7 across the 12 of their papers we have counts for
16 papers · 1 filter
A Characterization for Spectral and Trace Positivity of Matrix Words
Frederik Garbe, Fan Wei
In this paper, we provide a complete structural characterization of which words in noncommuting matrix variables and their formal transposes universally evaluate to matrices with n…
Hamiltonicity of inhomogeneous random graphs
Frederik Garbe, Jan Hladký, Simón Piga
We provide a complete characterization of those graphons for which the inhomogeneous random graph \(\G(n,W)\) is asymptotically almost surely Hamiltonian. The characterization…
Infinitely many counterexamples to a conjecture of Lovász
Aida Abiad, Frederik Garbe, Xavier Povill +1
Motivated by the well-known conjecture of Ryser which relates maximum matchings to minimum vertex covers in -partite -uniform hypergraphs, Lovász formulated a stronger conjec…
Graph factors and powers of Hamilton cycles in the budget-constrained random graph process
Alberto Espuny Díaz, Frederik Garbe, Tássio Naia +1
We consider the following budget-constrained random graph process introduced by Frieze, Krivelevich and Michaeli. A player, called Builder, is presented with distinct edges of…
Asymptotically Enumerating Independent Sets in Regular -Partite -Uniform Hypergraphs
Patrick Arras, Frederik Garbe, Felix Joos
The number of independent sets in regular bipartite expander graphs can be efficiently approximated by expressing it as the partition function of a suitable polymer model and trunc…
A tower lower bound for the degree relaxation of the Regularity Lemma
Frederik Garbe, Jan Hladký
It is well-known that if is an -regular pair (in the sense of Szemerédi) then there exist sets and with $|A'|\leq \vare…
Hypergraphs with uniform Turán density equal to 8/27
Frederik Garbe, Daniel Iľkovič, Daniel Kráľ +2
In the 1980s, Erdős and Sós initiated the study of Turán problems with a uniformity condition on the distribution of edges: the uniform Turán density of a hypergraph is the inf…
The dimension of the feasible region of pattern densities
Frederik Garbe, Daniel Kral, Alexandru Malekshahian +1
A classical result of Erdős, Lovász and Spencer from the late 1970s asserts that the dimension of the feasible region of densities of graphs with at most k vertices in large graphs…
On pattern-avoiding permutons
Frederik Garbe, Jan Hladký, Gábor Kun +1
The theory of limits of permutations leads to limit objects called permutons, which are certain Borel measures on the unit square. We prove that permutons avoiding a given permutat…
From flip processes to dynamical systems on graphons
Frederik Garbe, Jan Hladký, Matas Šileikis +1
We introduce a class of random graph processes, which we call flip processes. Each such process is given by a rule which is a function $\mathcal{R}:\mathcal{H}_k\rightarrow \mathca…
Hypergraphs with minimum positive uniform Turán density
Frederik Garbe, Daniel Kral, Ander Lamaison
Reiher, Rödl and Schacht [J. London Math. Soc. 97 (2018), 77--97] showed that the uniform Turán density of every -uniform hypergraph is either or at least , and asked…
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…
Longest paths in random hypergraphs
Oliver Cooley, Frederik Garbe, Eng Keat Hng +3
Given integers with , we consider the length of the longest -tight path in the binomial random -uniform hypergraph . We show that this length…
Two remarks on graph norms
Frederik Garbe, Jan Hladký, Joonkyung Lee
For a graph , its homomorphism density in graphs naturally extends to the space of two-variable symmetric functions in , , denoted by . One may then…
Contagious sets in a degree-proportional bootstrap percolation process
Frederik Garbe, Andrew McDowell, Richard Mycroft
We study the following bootstrap percolation process: given a connected graph , a constant and an initial set of \emph{infected} vertices, at ea…
Hamilton cycles in hypergraphs below the Dirac threshold
Frederik Garbe, Richard Mycroft
We establish a precise characterisation of -uniform hypergraphs with minimum codegree close to which contain a Hamilton -cycle. As an immediate corollary we identify th…