Isoperimetric inequalities and the width parameters of graphs

Authors:
L. Sunil Chandran;T. Kavitha;C. R. Subramanian
Affiliations:
Max-Planck-Institute für Informatik, Saarbrücken, Germany;Max-Planck-Institute für Informatik, Saarbrücken, Germany;The Institute of Mathematical Sciences, Chennai, India
Venue:
COCOON'03 Proceedings of the 9th annual international conference on Computing and combinatorics
Year:
2003

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Abstract

We relate the isoperimetric inequalities with many width parameters of graphs: treewidth, pathwidth and the carving width. Using these relations, we deduce 1. A lower bound for the treewidth in terms of girth and average degree 2. The exact values of the pathwidth and carving width of the d- dimensional hypercube, Hd 3. That treewidth (Hd) = Θ (2d/√d). Moreover we study these parameters in the case of a generalization of hypercubes, namely the Hamming graphs.