The rotation graph of k-ary trees is Hamiltonian

Authors:
Clemens Huemer;Ferran Hurtado;Julian Pfeifle
Affiliations:
Departament de Matemàtica Aplicada IV, Universitat Politècnica de Catalunya, Spain;Departament de Matemàtica Aplicada II, Universitat Politècnica de Catalunya, Spain;Departament de Matemàtica Aplicada II, Universitat Politècnica de Catalunya, Spain
Venue:
Information Processing Letters
Year:
2008

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Abstract

In this paper we show that the graph of k-ary trees, connected by rotations, contains a Hamilton cycle. Our proof is constructive and thus provides a cyclic Gray code for k-ary trees. Furthermore, we identify a basic building block of this graph as the 1-skeleton of the polytopal complex dual to the lower faces of a certain cyclic polytope.