37 citations · 92 across the 9 of their papers we have counts for
6 papers · 1 filter
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…
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…
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…
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…