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Some results on tree decomposition of graphs

✍ Scribed by Guoli Ding; Bogdan Oporowski

Publisher: John Wiley and Sons
Year: 1995
Tongue: English
Weight: 968 KB
Volume: 20
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.3190200412

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✦ Synopsis

Abstract

We investigate tree decompositions (T,(X~t~)~tϵV(T)~) whose width is “close to optimal” and such that all the subtrees of T induced by the vertices of the graph are “small.” We prove the existence of such decompositions for various interpretations of “close to optimal” and “small.” As a corollary of these results, we prove that the dilation of a graph is bounded by a logarithmic function of the congestion of the graph thereby settling a generalization of a conjecture of Bienstock. © 1995 John Wiley & Sons, Inc.

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