Abstract
In this paper, we present a one-to-one embedding of a graph with bounded treewidth into its optimal hypercube. This is the first time that embeddings of graphs with a very irregular structure into hypercubes are investigated. The dilation of the presented embedding is bounded by 3 ⌈log((d+1) (t+1))⌉+8, where t denotes the treewidth of the graph and d denotes the maximal degree of a vertex in the graph. Moreover, if the graph has constant treewidth or is represented by a tree-decomposition of width t, this embedding can be efficiently implemented on the optimal hypercube itself.KeywordsBinary TreeDecomposition TreeComplete Binary TreeMarked VertexHost GraphThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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