32 citations · 60 across the 8 of their papers we have counts for
7 papers · 1 filter
On the contractibility of random Vietoris-Rips complexes
Tobias Müller, Matěj Stehlík
We show that the Vietoris-Rips complex built over points sampled at random from a uniformly positive probability measure on a convex body $K\subseteq \mathbb…
Component Games on Random Graphs
Rani Hod, Michael Krivelevich, Tobias Müller +2
In the component game played on a graph , two players, Maker and Breaker, alternately claim~ and~ previously unclaimed edges of , respectively. Maker…
Limiting probabilities of first order properties of random sparse graphs and hypergraphs
Alberto Larrauri, Tobias Müller, Marc Noy
Let be the binomial random graph in the sparse regime, which as is well-known undergoes a phase transition at . Lynch (Random Structures Algorithms, 1992) s…
The first order convergence law fails for random perfect graphs
Tobias Müller, Marc Noy
We consider first order expressible properties of random perfect graphs. That is, we pick a graph uniformly at random from all (labelled) perfect graphs on vertices and c…
Generalised Mycielski graphs and the Borsuk-Ulam theorem
Tobias Müller, Matěj Stehlík
Stiebitz determined the chromatic number of generalised Mycielski graphs using the topological method of Lovasz, which invokes the Borsuk-Ulam theorem. Van Ngoc and Tuza used eleme…
Logical limit laws for minor-closed classes of graphs
Peter Heinig, Tobias Muller, Marc Noy +1
Let be an addable, minor-closed class of graphs. We prove that the zero-one law holds in monadic second-order logic (MSO) for the random graph drawn uniformly at rando…
Cops and Robbers on Geometric Graphs
Andrew Beveridge, Andrzej Dudek, Alan Frieze +1
Cops and robbers is a turn-based pursuit game played on a graph . One robber is pursued by a set of cops. In each round, these agents move between vertices along the edges of th…