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Boxicity of Graphs on Surfaces

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Abstract

The boxicity of a graph G = (V, E) is the least integer k for which there exist k interval graphs G i  = (V, E i ), 1 ≤ i ≤ k, such that \({E = E_1 \cap \cdots \cap E_k}\) . Scheinerman proved in 1984 that outerplanar graphs have boxicity at most two and Thomassen proved in 1986 that planar graphs have boxicity at most three. In this note we prove that the boxicity of toroidal graphs is at most 7, and that the boxicity of graphs embeddable in a surface Σ of genus g is at most 5g + 3. This result yields improved bounds on the dimension of the adjacency poset of graphs on surfaces.

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Authors and Affiliations

  1. Laboratoire G-SCOP, CNRS, Grenoble-INP, Grenoble, France

    Louis Esperet

  2. Département d’Informatique, Université Libre de Bruxelles, Brussels, Belgium

    Gwenaël Joret

Authors
  1. Louis Esperet
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  2. Gwenaël Joret
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Correspondence to Louis Esperet.

Additional information

This work was supported in part by the Actions de Recherche Concertées (ARC) fund of the Communauté française de Belgique. L. Esperet is partially supported by ANR Project Heredia under Contract anr-10-jcjc-heredia. G. Joret is a Postdoctoral Researcher of the Fonds National de la Recherche Scientifique (F.R.S.–FNRS).

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Esperet, L., Joret, G. Boxicity of Graphs on Surfaces. Graphs and Combinatorics 29, 417–427 (2013). https://doi.org/10.1007/s00373-012-1130-x

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  • DOI: https://doi.org/10.1007/s00373-012-1130-x

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