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Discrete Mathematics
Article
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Discrete Mathematics
Article . 2006
License: Elsevier Non-Commercial
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Discrete Mathematics
Article . 2006 . Peer-reviewed
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The treewidth and pathwidth of hypercubes

Authors: L. Sunil Chandran; Telikepalli Kavitha;

The treewidth and pathwidth of hypercubes

Abstract

AbstractThe d-dimensional hypercube, Hd, is the graph on 2d vertices, which correspond to the 2d d-vectors whose components are either 0 or 1, two of the vertices being adjacent when they differ in just one coordinate. The notion of Hamming graphs (denoted by Kqd) generalizes the notion of hypercubes: The vertices correspond to the qd d-vectors where the components are from the set {0,1,2,…,q-1}, and two of the vertices are adjacent if and only if the corresponding vectors differ in exactly one component. In this paper we show that the pw(Hd)=∑m=0d-1mm2 and the tw(Kqd)=θ(qd/d).

Keywords

Hypercube, Hamming graph, Treewidth, Discrete Mathematics and Combinatorics, Pathwidth, Theoretical Computer Science

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
34
Top 10%
Top 10%
Top 10%
hybrid