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Isoperimetric Inequalities and the Width Parameters of Graphs

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Computing and Combinatorics (COCOON 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2697))

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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. 1.

    A lower bound for the treewidth in terms of girth and average degree

  2. 2.

    The exact values of the pathwidth and carving width of the d-dimensional hypercube, H d

  3. 3.

    That treewidth \( (H_d ) = \Theta \left( {\frac{{2^d }} {{\sqrt d }}} \right) \).

Moreover we study these parameters in the case of a generalization of hypercubes, namely the Hamming graphs.

This is a combined announcement of the results in two different papers. The results explained in Section 3 is from Girth and Treewidth (L. S. Chandran, C. R. Subramanian) 8. The rest of the results are from Lower bounds for width parameters of graphs using Isoperimetric Inequalities (L.S. Chandran, T. Kavitha) 7.

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Author information

Authors and Affiliations

  1. Max-Planck-Institute für Informatik, Stuhlsatzenhausweg 85, 66123, Saarbrücken, Germany

    L. Sunil Chandran & T. Kavitha

  2. The Institute of Mathematical Sciences, Chennai, 600113, India

    C. R. Subramanian

Authors
  1. L. Sunil Chandran
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  2. T. Kavitha
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  3. C. R. Subramanian
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Texas at Austin, One University Station, C0500, Austin, TX, 78712, USA

    Tandy Warnow

  2. Department of Computer Science, Montana State University, EPS 357, Bozeman, MT, 59717, USA

    Binhai Zhu

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© 2003 Springer-Verlag Berlin Heidelberg

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Sunil Chandran, L., Kavitha, T., Subramanian, C.R. (2003). Isoperimetric Inequalities and the Width Parameters of Graphs. In: Warnow, T., Zhu, B. (eds) Computing and Combinatorics. COCOON 2003. Lecture Notes in Computer Science, vol 2697. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45071-8_39

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  • DOI: https://doi.org/10.1007/3-540-45071-8_39

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40534-4

  • Online ISBN: 978-3-540-45071-9

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