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Algorithms for Generating Strongly Chordal Graphs

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Transactions on Computational Science XXXVIII

Part of the book series: Lecture Notes in Computer Science ((TCOMPUTATSCIE,volume 12620))

Abstract

Graph generation serves many useful purposes: cataloguing, testing conjectures, to which we would like to add that of producing test instances for graph algorithms. Strongly chordal graphs are a subclass of chordal graphs for which polynomial-time algorithms could be designed for problems which are NP-complete for the parent class of chordal graphs. In this paper, we propose three different algorithms for generating strongly chordal graphs, each based on a different characterization of strongly chordal graphs. Each one of them is interesting in its own right, but the third one has turned out to be the most versatile in the sense that it can generate strongly chordal graphs with multiple components and does not require a chordal graph as input.

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Author information

Authors and Affiliations

  1. School of Computer Science, University of Windsor, Windsor, Canada

    Asish Mukhopadhyay & Md. Zamilur Rahman

Authors
  1. Asish Mukhopadhyay
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  2. Md. Zamilur Rahman
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Corresponding author

Correspondence to Asish Mukhopadhyay .

Editor information

Editors and Affiliations

  1. University of Calgary, Calgary, AB, Canada

    Marina L. Gavrilova

  2. Sardina Systems OÜ, Tallinn, Estonia

    C.J. Kenneth Tan

Appendix

Appendix

See Figs. 21, 22,  23 and 24.

Fig. 21.
figure 21

Strongly chordal graphs generated by the first method

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Fig. 22.
figure 22

Strongly chordal graphs generated by the second method that adds a minimal number of edges to a trampoline

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Fig. 23.
figure 23

Strongly chordal graphs generated by the second method that adds a user-specified number of edges to a trampoline using the completion procedure

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Fig. 24.
figure 24

Strongly chordal graphs generated by the third method

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Mukhopadhyay, A., Rahman, M.Z. (2021). Algorithms for Generating Strongly Chordal Graphs. In: Gavrilova, M.L., Tan, C.K. (eds) Transactions on Computational Science XXXVIII. Lecture Notes in Computer Science(), vol 12620. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-63170-6_4

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  • DOI: https://doi.org/10.1007/978-3-662-63170-6_4

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-63169-0

  • Online ISBN: 978-3-662-63170-6

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