Let V = \left\{v_1, ... ,v_n\right\} be a collection of vertices in the plane. Define the maximum convex hull C of V to be the convex polygon with vertices in V such that every point in V is either an interior point or a vertex of C.

Define C_1=\left\{v_1, ... v_m\right\} to be the maximum convex hull of V relabling if necessary. With the remaining points V/ C_1 = \left\{v_{m+1}, ..., v_n\right\} recursively define maximum convex hulls C_2, ..., C_k.

The picture should be a series of shrinking polygons each completely contained in the previous. Some of this requires proof but I don't think it is too difficult to show that given any finite collection of points in the plane there exists a unique maximum convex hull.

What I would like to do is connect the convex hulls in some minimum way (minimum number of edges) to ensure the resulting graph contains a complete cycle.

Idea:
\forall i, \forall v \in C_i connect v \text{ to } x \in C_{i+1} such that d(v,x) <= d(v,y), \text{ } \forall y \in C_{i+1}
In other words connect each vertex on each hull to the closest vertex on the next hull.