A sufficient condition for the existence of plane spanning trees on geometric graphs
2013
Let P be a set of n>=3 points in general position in the plane and let G be a geometric graph with vertex set P. If the number of empty triangles @Duvw 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.
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