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Article Dans Une Revue Czechoslovak Mathematical Journal Année : 2014

A note on the cubical dimension of new classes of binary trees

Kamal Kabyl
  • Fonction : Auteur
Abdelhafid Berrachedi
  • Fonction : Auteur

Résumé

The cubical dimension of a graph G is the smallest dimension of a hypercube into which G is embeddable as a subgraph. The conjecture of Havel [On hamiltonian circuits and spanning trees of hypercubes. ˇ Casopis ˇ Pest. Mat 109 (2) (1984) 135-152] claims that the cubical dimension of every balanced binary tree with 2n vertices, n 1, is n. The 2-rooted complete binary tree of depth n is obtained from two copies of the complete binary tree of depth n by adding an edge linking their respective roots. In this paper, we determine the cubical dimen- sion of trees obtained by subdividing twice a 2-rooted complete binary tree and prove that every such balanced tree satisfies the conjecture of Havel.

Dates et versions

hal-00881273 , version 1 (08-11-2013)

Identifiants

Citer

Kamal Kabyl, Abdelhafid Berrachedi, Eric Sopena. A note on the cubical dimension of new classes of binary trees. Czechoslovak Mathematical Journal, 2014, 65 (1), pp.151-160. ⟨10.1007/s10587-015-0165-6⟩. ⟨hal-00881273⟩

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