The rotation graph of k-ary trees is Hamiltonian
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. (C) 2008 Elsevier B.V. All rights reserved.
k-ary trees gray code combinatorial problems polygon dissections