An alpha shape starts with a Delaunay triangulation. Then some parts of it are deleted as defined by the alpha shape. (Having written alpha shape tools myself, I know of what I speak.) But we can see that it does exactly that, based on an example.
XY = rand(100,2);
DT = delaunayTriangulation(XY);
T = alphaShape(XY,.15);
plot(T)
hold on
triplot(DT.ConnectivityList,DT.Points(:,1),DT.Points(:,2),'r')
See that the two triangulations are the same, where a triangle remains from the alpha shape. The alpha shape plot would have the edges in black there, but they are entirely hidden by the red edges from triplot.
As I said, it starts with the Delaunay triangulation, then deletes. So that which remains is indeed a pure subset of the Delaunay triangulation.
