Isometric embeddings of subidivided complete graphs in the hypercube
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.
Domaines
Combinatoire [math.CO]
Origine : Fichiers produits par l'(les) auteur(s)