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6 votes
2 answers
404 views

Estimating shortest paths in planar drawings of graphs

Consider a drawing (in $\mathbb{R}^2$) of a planar graph. (The drawing is given, contrarily to the common setup in graph theory where we are seeking to build a drawing with specific properties.) For ...
Denis Gorodkov's user avatar
5 votes
6 answers
435 views

Characterizing Convex Configurations of Quadrupels of Coplanar Points via Linear (In-)equalities between Distance Sums or Differences

Given 4 points $A$, $B$, $C$ and $D$ in general position in the euclidean plane, is it possible to determine from the 6 distances $AB$, $BC$, $CD$, $AD$, $AC$ and, $BD$ alone, whether every point is a ...
Manfred Weis's user avatar
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1 vote
1 answer
3k views

3D Delaunay Triangulation -> Euclidean Minimum Spanning Tree

I read that the Euclidean Minimum Spanning Tree (EMST) of a set of points is a subgraph of any Delaunay triangulation. Apparently the easiest/fastest way to obtain the EMST is to find the Deluanay ...
David Doria's user avatar