Geometry of partial cube graphs

author: David Eppstein, University of California, Irvine
published: Sept. 7, 2007,   recorded: September 2007,   views: 5074


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Partial cubes are graphs defined by a geometric structure: the graph vertices can be placed on the vertices of a hypercube in such a way that graph distance equals Hamming distance. We survey recent developments in the theory of these graphs that relate them in other ways to geometric structures: lattice embeddings, hyperplane arrangements, systems of translated quadrants in the plane, and flip graphs of triangulations.

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