9 citations · 21 across the 18 of their papers we have counts for
6 papers · 1 filter
A Note on the 2-Colored Rectilinear Crossing Number of Random Point Sets in the Unit Square
Sergio Cabello, Éva Czabarka, Ruy Fabila-Monroy +5
Let be a set of four points chosen independently, uniformly at random from a square. Join every pair of points of with a straight line segment. Color these edges red if the…
Reconfiguration of plane trees in convex geometric graphs
Nicolas Bousquet, Lucas De Meyer, Théo Pierron +1
A non-crossing spanning tree of a set of points in the plane is a spanning tree whose edges pairwise do not cross. Avis and Fukuda in 1996 proved that there always exists a flip se…
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…
Maximum Independent Set when excluding an induced minor: and
Édouard Bonnet, Julien Duron, Colin Geniet +2
Dallard, Milanič, and Štorgel [arXiv '22] ask if for every class excluding a fixed planar graph as an induced minor, Maximum Independent Set can be solved in polynomial time, a…
A note on highly connected -minor free graphs
Nicolas Bousquet, Théo Pierron, Alexandra Wesolek
We show that every -connected -minor free graph with minimum degree at least has maximum degree at most . As a consequence, we show that every 3-connected…