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Article Dans Une Revue SIAM Journal on Discrete Mathematics Année : 2008

Isometric embeddings of subidivided complete graphs in the hypercube

Laurent Beaudou
Sylvain Gravier
Kahina Meslem
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Résumé

Isometric subgraphs of hypercubes are known as partial cubes. These graphs have first been investigated by Graham and Pollack and Djokovic. Several papers followed with various characterizations of partial cubes. In this paper, it is proven that a subdivision of a complete graph of order n (n > 3), is a partial cube if and only if it is isomorphic to S(Kn), or there exist n-1 non-subdivided edges of Kn adjacent to a common vertex in the subdivision and the other edges of Kn are subdivided an odd number of times. A huge family of partial cubes is then obtained as a corollary from any arbitrary oddly subdivided graph.
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Dates et versions

hal-00187039 , version 1 (13-11-2007)

Identifiants

Citer

Laurent Beaudou, Sylvain Gravier, Kahina Meslem. Isometric embeddings of subidivided complete graphs in the hypercube. SIAM Journal on Discrete Mathematics, 2008, 22, pp.1226--1238. ⟨10.1137/070681909⟩. ⟨hal-00187039⟩

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