9 papers
Graph factors and powers of Hamilton cycles in the budget-constrained random graph process
Alberto Espuny DÃaz, 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…
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 is asymptotically almost surely Hamiltonian. The characterization inv…
Hypergraphs with uniform Turán density equal to 8/27
Frederik Garbe, Daniel IľkoviÄ, Daniel Kráľ +2
In the 1980s, ErdÅs 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…
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 conje…
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…