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{\bf Juhani Nieminen, Matti Peltola and Pasi Ruotsalainen}
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{\bf Two Characterizations of Hypercubes}
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Two characterizations of hypercubes are given: 1)~A graph is a
hypercube if and only if it is antipodal and bipartite $(0,2)$-graph.
2)~A graph is an $n$-hypercube if and only if there are $n$ pairs of
prime convexes, the graph is a prime convex intersection graph, and
each intersection of $n$ prime convexes (no one of which is from the
same pair) is a vertex.



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