A sufficient condition for the existence of plane spanning trees on geometric graphs (1202.3385v1)

Abstract: Let P be a set of n > 2 points in general position in the plane and let G be a geometric graph with vertex set P. If the number of empty triangles uvw in P for which the subgraph of G induced by {u,v,w} is not connected is at most n-3, then G contains a non-self intersecting spanning tree.