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Ponencia
Triangulations without pointed spanning trees
(2004)
Problem 50 in the Open Problems Project asks whether any triangulation on a point set in the plane contains a pointed spanning tree as a subgraph. We provide a counterexample. As a consequence we show that there ...
Ponencia
On the number of pseudo-triangulations of certain point sets
(2004)
We compute the exact number of pseudo-triangulations for two prominent point sets, namely the so-called double circle and the double chain. We also derive a new asymptotic lower bound for the maximal number of pseudotriangulations ...
Ponencia
A quadratic distance bound on sliding between crossing-free spanning trees
(2004)
Let S be a set of n points in the plane and let TS be the set of all crossing-free spanning trees of S. We show that any two trees in TS can be transformed into each other by O(n2) local and constant-size edge slide ...