Partial cubes and their τ-graphs

  • Authors:

  • Sandi Klavar;Matja Kovše

  • Affiliations:

  • Department of Mathematics and Computer Science, PeF, University of Maribor, Koroška cesta 160, 2000 Maribor, Slovenia;Institute of Mathematics, Physics and Mechanics, Jadranska 19, 1000 Ljubljana, Slovenia

  • Venue:
  • European Journal of Combinatorics
  • Year:
  • 2007

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Abstract

The @t-graph G^@t of a partial cube G has the equivalence classes of the Djokovic-Winkler relation as vertices, two classes E and F being adjacent if some edges e@?E and f@?F induce a convex P"3. It is shown that for every graph G there exists a median graph M such that G=M^@t, that G^@t is connected if and only if G is a Cartesian prime graph, and that for a median graph G its @t-graph is K"n-free if and only if G contains no convex K"1","n.