Tiled partial cubes

  • Authors:

  • Boštjan Brešar;Wilfried Imrich;Sandi Klavžar;Henry Martyn Mulder;Riste Škrekovski

  • Affiliations:

  • University of Maribor, FK Vrbanska 30, 2000 Maribor, Slovenia;Montanuniversität Leoben A-8700 Leoben, Austria;Department of Mathematics, PEF University of Maribor, Koroška cesta 160, 2000 Maribor, Slovenia;Econometrisch Instituut, Erasmus Universiteit P.O. Box 1738, 3000 DR Rotterdam, The Netherlands;Department of Mathematics, University of Ljubljana, Jadranska 19, 1111 Ljubljana, Slovenia

  • Venue:
  • Journal of Graph Theory
  • Year:
  • 2002

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Abstract

In the quest to better understand the connection between median graphs, triangle-free graphs and partial cubes, a hierarchy of subclasses of partial cubes has been introduced. In this article, we study the role of tiled partial cubes in this scheme. For instance, we prove that almost-median graphs are tiled and that tiled partial cubes are semi-median. We also describe median graphs as tiled partial cubes without convex Q3- and extend an inequality for median graphs to a larger subclass of partial cubes. © 2002 Wiley Periodicals, Inc. J Graph Theory 40: 91–103, 2002