Strong Isometric Dimension, Biclique Coverings, and Sperner's Theorem

  • Authors:

  • Dalibor Fronček;Janja Jerebic;Sandi Klavžar;Petr Kovář

  • Affiliations:

  • Department of Mathematics and Statistics, University of Minnesota Duluth, 1117 University Drive, Duluth, MN 55812, USA (e-mail: dfroncek@d.umn.edu);Department of Mathematics and Computer Science, PeF, University of Maribor, Korošska cesta 160, 2000 Maribor, Slovenia (e-mail: janja.jerebic@uni-mb.si, sandi.klavzar@uni-mb.si);Department of Mathematics and Computer Science, PeF, University of Maribor, Korošska cesta 160, 2000 Maribor, Slovenia (e-mail: janja.jerebic@uni-mb.si, sandi.klavzar@uni-mb.si);Department of Mathematics and Descriptive Geometry, Technical University of Ostrava, 17. listopadu 15, 708 33 Ostrava-Poruba, Czech Republic (e-mail: petr.kovar@vsb.cz)

  • Venue:
  • Combinatorics, Probability and Computing
  • Year:
  • 2007

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Abstract

The strong isometric dimension of a graph $G$ is the least number $k$ such that $G$ isometrically embeds into the strong product of $k$ paths. Using Sperner's theorem, the strong isometric dimension of the Hamming graphs $K_2\,{\square}\, K_n$ is determined.