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Article Dans Une Revue Computing in Geometry and Topology Année : 2023

A Note on the Flip Distance between Non-crossing Spanning Trees

Résumé

We consider spanning trees of n points in convex position whose edges are pairwise non-crossing. Applying a flip to such a tree consists in adding an edge and removing another so that the result is still a non-crossing spanning tree. Given two trees, we investigate the minimum number of flips required to transform one into the other. The naive 2n - Omega(1) upper bound stood for 25 years until a recent breakthrough from Aichholzer et al. yielding a 2n - Ω(log n) bound. We improve their result with a 2n - Ω(√n) upper bound, and we strengthen and shorten the proofs of several of their results.

Dates et versions

hal-04323643 , version 1 (05-12-2023)

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Nicolas Bousquet, Valentin Gledel, Jonathan Narboni, Théo Pierron. A Note on the Flip Distance between Non-crossing Spanning Trees. Computing in Geometry and Topology, 2023, ⟨10.57717/cgt.v2i1.36⟩. ⟨hal-04323643⟩
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