Reverse search for enumeration
Discrete Applied Mathematics - Special volume: first international colloquium on graphs and optimization (GOI), 1992
Geometric tree graphs of points in convex position
Discrete Applied Mathematics - Special issue on the 13th European workshop on computational geometry CG '97
Lower bounds on the number of crossing-free subgraphs of KN
Computational Geometry: Theory and Applications
Sequences of spanning trees and a fixed tree theorem
Computational Geometry: Theory and Applications - Special issue on: Sixteenth European Workshop on Computational Geometry (EUROCG-2000)
Graphs of Triangulations and Perfect Matchings
Graphs and Combinatorics
Transforming spanning trees and pseudo-triangulations
Information Processing Letters
A quadratic distance bound on sliding between crossing-free spanning trees
Computational Geometry: Theory and Applications
Amortized efficiency of generating planar paths in convex position
Theoretical Computer Science
Bichromatic compatible matchings
Proceedings of the twenty-ninth annual symposium on Computational geometry
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For a planar point set we consider the graph whose vertices are the crossing-free straight-line spanning trees of the point set, and two such spanning trees are adjacent if their union is crossing-free. An upper bound on the diameter of this graph implies an upper bound on the diameter of the flip graph of pseudo-triangulations of the underlying point set. We prove a lower bound of @W(logn/loglogn) for the diameter of the transformation graph of spanning trees on a set of n points in the plane. This nearly matches the known upper bound of O(logn). If we measure the diameter in terms of the number of convex layers k of the point set, our lower bound construction is tight, i.e., the diameter is in @W(logk) which matches the known upper bound of O(logk). So far only constant lower bounds were known.