Abstract
Let G and H be two simple undirected graphs. An embedding of the graph G in the graph H is an injective mapping f from the vertices of G into the vertices of H together with a mapping Pf of edges of G into paths in H. The dilation of the embedding is the maximum taken over all the lengths of the paths Pf(x,y) associated with the edges (x,y) of G.
One challenge pointed out in [9] is to find embeddings of the de Bruijn graph in the hypercube of the same order which have a low dilation. For a de Bruijn graph of diameter D we give an embedding in a hypercube of the same diameter of dilation 2[D/51], and determine the edge-congestion and vertex-congestion of this embedding. Similar results are given for the shuffle-exchange graphs.
The work was supported partially by NSERC of Canada and by PRC C3 of France and was partially done while the third author was visiting the University of Paris-Sud.
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Baumslag, M., Heydemann, M.C., Opatrny, J., Sotteau, D. (1991). Embeddings of shuffle-like graphs in hypercubes. In: Aarts, E.H.L., van Leeuwen, J., Rem, M. (eds) Parle ’91 Parallel Architectures and Languages Europe. Lecture Notes in Computer Science, vol 505. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-25209-3_13
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DOI: https://doi.org/10.1007/978-3-662-25209-3_13
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