Geodesic
Recognizing Partial Cubes in Quadratic Time
Journal of Graph Algorithms and Applications, Tome 15 (2011) no. 2, pp. 269-293.

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We show how to test whether a graph with n vertices and m edges is a partial cube, and if so how to find a distance-preserving embedding of the graph into a hypercube, in the near-optimal time bound O(n2), improving previous O(nm)-time solutions.
DOI : 10.7155/jgaa.00226
Keywords: partial cube, isometric embedding, hypercube, distance labeling 
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David Eppstein. Recognizing Partial Cubes in Quadratic Time. Journal of Graph Algorithms and Applications, Tome 15 (2011) no. 2, pp. 269-293. doi : 10.7155/jgaa.00226. http://geodesic.mathdoc.fr/articles/10.7155/jgaa.00226/

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