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Two characterizations of hypercubes. (English) Zbl 1217.05195

Summary: 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.

MSC:

05C75 Structural characterization of families of graphs
05C65 Hypergraphs
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