Given:

1. The nearest neighbor of 𝑝𝑖 then 𝑝𝑖-𝑝𝑗 is a Delaunay edge.

2. In a 3D set of points, if we know that consecutive points ie... 𝑝𝑖-𝑝i+1 are nearest neighbors.

3. The 3D points do not form a straight line

Assumption:

Each Delaunay tesselation (3D) has at least 2 nearest neighbor edges.

Is my assumption true? If not can you please explain to me the possible exceptions?

Thanks,

Pranav

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