37 citations · 92 across the 9 of their papers we have counts for
12 papers
Non-vanishing uniqueness threshold for hyperbolic Poisson-Voronoi percolation in dimension at least three
Matthias Irlbeck, Tobias Müller
We study the threshold for the existence of exactly one unbounded cluster for Poisson-Voronoi percolation on the -dimensional hyperbolic space for . By r…
Clustering in a hyperbolic model of complex networks
Nikolaos Fountoulakis, Pim van der Hoorn, Tobias Müller +1
In this paper we consider the clustering coefficient and clustering function in a random graph model proposed by Krioukov et al.~in 2010. In this model, nodes are chosen randomly i…
The diameter of KPKVB random graphs
Tobias Müller, Merlijn Staps
We consider a model for complex networks that was recently proposed as a model for complex networks by Krioukov et al. In this model, nodes are chosen randomly inside a disk in the…
Coloring Jordan regions and curves
Wouter Cames van Batenburg, Louis Esperet, Tobias Müller
A Jordan region is a subset of the plane that is homeomorphic to a closed disk. Consider a family of Jordan regions whose interiors are pairwise disjoint, and such th…
Law of large numbers for the largest component in a hyperbolic model of complex networks
Nikolaos Fountoulakis, Tobias Müller
We consider the component structure of a recent model of random graphs on the hyperbolic plane that was introduced by Krioukov et al. The model exhibits a power law degree sequence…
On r-dynamic Coloring of Grids
Ross Kang, Tobias Muller, Douglas B. West
An \textit{-dynamic -coloring} of a graph is a proper -coloring of such that every vertex in has neighbors in at least different color clas…
The acquaintance time of (percolated) random geometric graphs
Tobias Muller, Pawel Pralat
In this paper, we study the acquaintance time $\AC(G)$ defined for a connected graph . We focus on $\G(n,r,p)$, a random subgraph of a random geometric graph in which vertic…
Maker-Breaker games on random geometric graphs
Andrew Beveridge, Andrzej Dudek, Alan Frieze +2
In a Maker-Breaker game on a graph , Breaker and Maker alternately claim edges of . Maker wins if, after all edges have been claimed, the graph induced by his edges has some…
Integer realizations of disk and segment graphs
Colin McDiarmid, Tobias Muller
A disk graph is the intersection graph of disks in the plane, a unit disk graph is the intersection graph of same radius disks in the plane, and a segment graph is an intersection…
On the chromatic number of random geometric graphs
Colin McDiarmid, Tobias Müller
Given independent random points $X_1,...,X_n\in\eR^d$ with common probability distribution , and a positive distance , we construct a random geometric graph with…
Acyclic Edge coloring of Planar Graphs
Manu Basavaraju, L. Sunil Chandran
An edge coloring of a graph is a proper edge coloring such that there are no bichromatic cycles. The \emph{acyclic chromatic index} of a graph is the minimum number k suc…
Disjoint Hamilton cycles in the random geometric graph
Xavier Pérez-Giménez, Nicholas C. Wormald
We prove a conjecture of Penrose about the standard random geometric graph process, in which n vertices are placed at random on the unit square and edges are sequentially added in…