Geodesic
On Homeomorphic Embeddings of Km,n in the Cube
Canadian journal of mathematics, Tome 32 (1980) no. 3, pp. 644-652

Voir la notice de l'article provenant de la source Cambridge University Press

Homeomorphic embeddings of Kn in the m-cube were investigated in [6]. In particular, it was proved that any homeomorph of Kn+1 embedded in the m-cube has at least n2 edges. Furthermore, homeomorphic embeddings of Kn+1 having exactly n2 edges are unique up to isomorphism. In this paper a similar problem for the complete bipartite graph is considered.We adopt the notation and terminology of [5].All graphs considered are without loops and multiple edges.Let x = uv be an edge of a graph G; x will be called subdivided if it is replaced by a vertex ω and by edges uω and ωv. A graph G’ is called a subdivision of G if it is obtained from G by a subdivision of an edge of G. A refinement Ĝ of G, is a graph isomorphic to a graph obtained from G by a finite sequence of subdivisions. 
Hartman, Jehuda. On Homeomorphic Embeddings of Km,n in the Cube. Canadian journal of mathematics, Tome 32 (1980) no. 3, pp. 644-652. doi: 10.4153/CJM-1980-050-6
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