We prove that the computation of a combinatorial shortest path between two vertices of a
graph associahedron, introduced by Carr and Devadoss, is NP-hard. This resolves an open …

The associahedron A (G) of a graph G has the property that its vertices can be thought of as
the search trees on G and its edges as the rotations between two search trees. If G is a …

Let P be a convex polygon in the plane, and let T be a triangulation of P. An edge e in T is
called a diagonal if it is shared by two triangles in T. A flip of a diagonal e is the operation of …

Flip graphs are a ubiquitous class of graphs, which encode relations on a set of
combinatorial objects by elementary, local changes. Skeletons of associahedra, for instance …

Suchbäume auf Graphen (SBGs) sind eine weitreichende Verallgemeinerung binärer
Suchbäume. Bei SBGs ist der Suchraum ein Graph statt einer totalen Ordnung. Die Idee ist …

In this paper we investigate the structure of flip graphs on non-crossing perfect matchings in
the plane. Specifically, consider all non-crossing straight-line perfect matchings on a set of 2 …

Rotation distance between rooted binary trees measures the degree of similarity of two trees
with ordered leaves and is equivalent to edge-flip distance between triangular subdivisions …

Rotation distance between rooted binary trees measures the extent of similarity of two trees
with ordered leaves. There are no known polynomial-time algorithms for computing rotation …

We study restricted rotation distance between ternary and higher-valence trees using
approaches based upon generalizations of Thompson's group $ F $. We obtain bounds and …

The rotation distanced (S, T) between two binary trees S, T of n vertices is the minimum
number of rotations to transform S into T. While it is known that d (S, T)⩽ 2n− 6, a well-known …