4 papers
On the local resilience of random geometric graphs with respect to connectivity and long cycles
Alberto Espuny Díaz, Lyuben Lichev, Alexandra Wesolek
Given an increasing graph property , a graph is -resilient with respect to if, for every spanning subgraph where each vertex keeps…
Cops and Robber on Hyperbolic Manifolds
Vesna Iršič, Bojan Mohar, Alexandra Wesolek
The Cops and Robber game on geodesic spaces is a pursuit-evasion game with discrete steps which captures the behavior of the game played on graphs, as well as that of continuous pu…
On Minimizing the Energy of a Spherical Graph Representation
Matt DeVos, Danielle Rogers, Alexandra Wesolek
Graph representations are the generalization of geometric graph drawings from the plane to higher dimensions. A method introduced by Tutte to optimize properties of graph drawings…
Sharp threshold for embedding balanced spanning trees in random geometric graphs
Alberto Espuny Díaz, Lyuben Lichev, Dieter Mitsche +1
A rooted tree is balanced if the degree of a vertex depends only on its distance to the root. In this paper we determine the sharp threshold for the appearance of a large family of…