Geometric intersection graphs form an intriguing class of structures in which vertices represent geometric objects – such as line segments, discs, or curves – and an edge is established between two ...

Vertices arrive sequentially in space and are joined to existing vertices at random according to a preferential rule combining degree and spatial proximity. We investigate phase transitions in the ...

This lecture course is devoted to the study of random geometrical objects and structures. Among the most prominent models are random polytopes, random tessellations, particle processes and random ...

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In this paper we study the treewidth of the random geometric graph, obtained by dropping n points onto the square [0, √n]² and connecting pairs of points by an edge if their distance is at most r = ...

Given a planar, undirected, graph enumerate all of the faces of the graph. Can also be described as finding all of the polygons within the graph, or the minimum cycle basis, based on Geometric Tools ...

Revised: This Reviewed Preprint has been revised by the authors in response to the previous round of peer review; the eLife assessment and the public reviews have been updated where necessary by the ...