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Proof of the bandwidth conjecture of Bollobás and Komlós

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Abstract

In this paper we prove the following conjecture by Bollobás and Komlós: For every γ > 0 and integers r ≥ 1 and Δ, there exists β > 0 with the following property. If G is a sufficiently large graph with n vertices and minimum degree at least ((r − 1)/r + γ)n and H is an r-chromatic graph with n vertices, bandwidth at most β n and maximum degree at most Δ, then G contains a copy of H.

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Authors and Affiliations

  1. Zentrum Mathematik, Technische Universität München, Boltzmannstraße 3, 85747, Garching bei München, Germany

    Julia Böttcher & Anusch Taraz

  2. Institut für Informatik, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099, Berlin, Germany

    Mathias Schacht

Authors
  1. Julia Böttcher
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  2. Mathias Schacht
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  3. Anusch Taraz
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Correspondence to Anusch Taraz.

Additional information

J. Böttcher and A. Taraz were partially supported by DFG grant TA 309/2-1. M. Schacht was partially supported by DFG grant SCHA 1263/1-1.

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Böttcher, J., Schacht, M. & Taraz, A. Proof of the bandwidth conjecture of Bollobás and Komlós. Math. Ann. 343, 175–205 (2009). https://doi.org/10.1007/s00208-008-0268-6

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  • DOI: https://doi.org/10.1007/s00208-008-0268-6

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