2002
DOI: 10.1006/jagm.2002.1217
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Embedding Graphs with Bounded Treewidth into Their Optimal Hypercubes

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 highly irregular structure into hypercubes are investigated. The presented embedding achieves dilation of at most 3 log d + 1 t + 1 + 8 and nodecongestion of at most O d dt 3 , where t denotes the treewidth of the graph and d denotes the maximal degree of a vertex in the graph. Provided that the graph is given by its tree-decomposition the embedd… Show more

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Cited by 8 publications
(6 citation statements)
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“…So the only fact that remains to be verified is that the vertex expansion ratio of S(H) is a constant. S(H) has constant expansion which implies a treewidth Θ(n) [20], whereas S(H) has an ordered bipartite decomposition of bounded width. Therefore, treewidth and the width of an ordered bipartite decomposition are incomparable.…”
Section: Decomposition Of Series-parallel Graphsmentioning
confidence: 99%
“…So the only fact that remains to be verified is that the vertex expansion ratio of S(H) is a constant. S(H) has constant expansion which implies a treewidth Θ(n) [20], whereas S(H) has an ordered bipartite decomposition of bounded width. Therefore, treewidth and the width of an ordered bipartite decomposition are incomparable.…”
Section: Decomposition Of Series-parallel Graphsmentioning
confidence: 99%
“…The treewidth (respectively, pathwidth or circlewidth) of a graph G = (V , E) is the minimum width over all tree decompositions (respectively, path decompositions or circle decompositions) of G. The notions of treewidth and pathwidth of a graph was introduced by Robertson and Seymour in [33,34]. As shown in [23,24], graphs with bounded treewidth have small extended edge bisectors. LEMMA 5.3.…”
Section: Bounded Treewidth Pathwidth and Circlewidthmentioning
confidence: 99%
“…This implies the following theorems on embeddings. Again the bounds on the dilation can be improved by a more sophisticated analysis (see [23,24] for bounded treewidth). THEOREM 5.5.…”
Section: Bounded Treewidth Pathwidth and Circlewidthmentioning
confidence: 99%
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