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

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Abstract

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 (1984) 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 dimension of trees obtained by subdividing twice a 2-rooted complete binary tree and prove that every such balanced tree satisfies the conjecture of Havel.

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Author information

Authors and Affiliations

  1. Laboratory of Modeling and Optimization of Systems, University of Bejaia, 06000, Bejaia, Algeria

    Kamal Kabyl

  2. Faculty of Mathematics, U.S.T.H.B, B.P. 32, El Alia, Bab-Ezzouar, 16111, Algiers, Algeria

    Kamal Kabyl & Abdelhafid Berrachedi

  3. LaBRI, UMR5800, Univ. Bordeaux, F-33400, Talence, France

    Éric Sopena

  4. LaBRI, UMR5800, CNRS, F-33400, Talence, France

    Éric Sopena

Authors
  1. Kamal Kabyl
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  2. Abdelhafid Berrachedi
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  3. Éric Sopena
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Correspondence to Kamal Kabyl.

Additional information

Part of this research has been done while the first author was visiting Bordeaux University.

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Kabyl, K., Berrachedi, A. & Sopena, É. A note on the cubical dimension of new classes of binary trees. Czech Math J 65, 151–160 (2015). https://doi.org/10.1007/s10587-015-0165-6

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  • DOI: https://doi.org/10.1007/s10587-015-0165-6

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