This video was recorded at 6th Slovenian International Conference on Graph Theory, Bled 2007. 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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