Involve: A Journal of Mathematics
- Volume 8, Number 5 (2015), 763-770.
Expected maximum vertex valence in pairs of polygonal triangulations
Edge-flip distance between triangulations of polygons is equivalent to rotation distance between rooted binary trees. Both distances measure the extent of similarity of configurations. There are no known polynomial-time algorithms for computing edge-flip distance. The best known exact universal upper bounds on rotation distance arise from measuring the maximum total valence of a vertex in the corresponding triangulation pair obtained by a duality construction. Here we describe some properties of the distribution of maximum vertex valences of pairs of triangulations related to such upper bounds.
Involve, Volume 8, Number 5 (2015), 763-770.
Received: 6 March 2014
Revised: 17 October 2014
Accepted: 22 November 2014
First available in Project Euclid: 22 November 2017
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random binary trees
Chu, Timothy; Cleary, Sean. Expected maximum vertex valence in pairs of polygonal triangulations. Involve 8 (2015), no. 5, 763--770. doi:10.2140/involve.2015.8.763. https://projecteuclid.org/euclid.involve/1511370947