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Rational homotopy theory for computing colorability of simplicial complexes

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Applicable Algebra in Engineering, Communication and Computing Aims and scope

Abstract

We show that the vertex coloring problem for finite simplicial complexes can be translated into the algebraic homotopy problem of ellipticity for rational spaces. We follow the ideas of Lechuga–Murillo for the classical vertex coloring of graphs.

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References

  1. Dobrinskaya, N., Møller, J., Notbohm, D.: Vertex colorings of simplicial complexes (preprint). arXiv:1007.0710v1

  2. Félix, Y., Halperin, S., Thomas, J.C.: Rational Homotopy Theory, Graduate Texts in Mathematics, vol. 205, 4th edn. Springer, Berlin (2001)

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Author information

Authors and Affiliations

  1. Dep. Computación, Universidade da Coruña, Campus de Elviña, 15071, A Coruña, Spain

    Cristina Costoya

  2. Dep. Álgebra, Geometría y Topología, Universidad de Málaga, Campus de Teatinos, 29071, Málaga, Spain

    Antonio Viruel

Authors
  1. Cristina Costoya
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  2. Antonio Viruel
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Corresponding author

Correspondence to Antonio Viruel.

Additional information

First author is partially supported by Grant MTM2013-43687-P (European FEDER support included). Second author is partially supported by Grant MTM2013-41768-P (European FEDER support included), and JA Grant FQM-213. Both authors are partially supported by Xunta de Galicia Grant EM2013/016.

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Costoya, C., Viruel, A. Rational homotopy theory for computing colorability of simplicial complexes. AAECC 26, 207–212 (2015). https://doi.org/10.1007/s00200-014-0249-9

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  • DOI: https://doi.org/10.1007/s00200-014-0249-9

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