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The Vulcan Game of Kal-Toh: Finding or Making Triconnected Planar Subgraphs

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Fun with Algorithms (FUN 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7288))

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Abstract

In the game of Kal-toh depicted in the television series Star Trek: Voyager, players attempt to create convex polyhedra by adding to a jumbled collection of metal rods. Inspired by this fictional game, we formulate graph-theoretical questions about polyhedral subgraphs, i.e., subgraphs that are triconnected and planar. The problem of determining the existence of a polyhedral subgraph within a graph G is shown to be NP-complete, and we also give some non-trivial upper bounds for the problem of determining the minimum number of edge additions necessary to guarantee the existence of a polyhedral subgraph in G.

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References

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Authors and Affiliations

  1. University of Waterloo, Waterloo, ON, N2L 5G5, Canada

    Terry Anderson & Therese Biedl

Authors
  1. Terry Anderson
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  2. Therese Biedl
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Editor information

Editors and Affiliations

  1. School of Computer Science, Carleton University, 1125 Col. By Dr., K1S 5B6, Ottawa, ON, Canada

    Evangelos Kranakis

  2. Department of Mathematics and Computer Science, Wesleyan University, 06459, Middleton, CT, USA

    Danny Krizanc

  3. Dipartimento di Scienze Ambientali, Informatica e Statistica, Università Ca’ Foscari, Via Torino 155, 30172, Mestre (Ve), Italy

    Flaminia Luccio

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© 2012 Springer-Verlag Berlin Heidelberg

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Anderson, T., Biedl, T. (2012). The Vulcan Game of Kal-Toh: Finding or Making Triconnected Planar Subgraphs. In: Kranakis, E., Krizanc, D., Luccio, F. (eds) Fun with Algorithms. FUN 2012. Lecture Notes in Computer Science, vol 7288. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30347-0_4

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  • DOI: https://doi.org/10.1007/978-3-642-30347-0_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-30346-3

  • Online ISBN: 978-3-642-30347-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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