I. Havel and P. Liebl. Embedding the dichotomic tree into the n-cube. Casopis Pest. Mat. 97 (1972) 201-205.  Home/Search   Document Not in Database   Summary   Related Articles

....isometric embeddings into Q n , Firsov [5] showed that all trees are cubical, and also noted that all cubical graphs are bipartite. Later, Havel and Mor avek [16] discovered necessary and sufficient conditions that a graph be cubical. These conditions are given below. Using this, Havel and Liebl [14, 15] deduced that trees, rectangular meshes, and hexagonal meshes are cubical, and they gave embeddings of these. They also proved that a cycle is cubical if and only if it is even. These results have been rediscovered numerous times. The embeddings of rectangular meshes are quite simple and ....

....Havel and Liebl [15] showed that the cubical dimension of the complete binary tree T n with height n and 2 n 1 Gamma 1 nodes is a most n 2 for n 2, and Nebesky [21] later proved that cd(T n ) n 2 when n 2. Other bounds on cubical dimensions of specific trees appear in Havel and Liebl [14, 15] and Wagner [24] Afrati, Papadimitriou, and Papageorgiou [1] gave a polynomial time algorithm which embeds a tree into a cube with dimension at most the square of the cubical dimension of the tree, and they conjectured that the problem of calculating the cubical dimension of a tree is ....

I. Havel and P. Liebl. Embedding the dichotomic tree into the n-cube. Casopis Pest. Mat. 97 (1972) 201-205.

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