Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Tuesday, December 18, 2018, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Jean Cardinal (Université Libre de Bruxelles (ULB))

On the Diameter of Tree Associahedra

We consider a natural notion of search trees on graphs, which we show is ubiquitous in various areas of discrete mathematics and computer science. Search trees on graphs can be modified by local operations called rotations, which generalize rotations in binary search trees. The rotation graph of search trees on a graph G is the skeleton of a polytope called the graph associahedron of G.

We will review known results on associahedra, then consider graph associahedra where the graph G is a tree. We construct a family of trees G on n vertices and pairs of search trees on G such that the minimum number of rotations required to transform one search tree into the other is Ω(n log n). This implies that the worst-case diameter of tree associahedra is Θ(n log n), which answers a question from Thibault Manneville and Vincent Pilaud.

Joint work with Stefan Langerman and Pablo Pérez-Lantero, to appear in the Electronic Journal of Combinatorics.

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