The vulcan game of kal-toh: finding or making triconnected planar subgraphs

Authors:
Terry Anderson;Therese Biedl
Affiliations:
University of Waterloo, Waterloo, ON, Canada;University of Waterloo, Waterloo, ON, Canada
Venue:
FUN'12 Proceedings of the 6th international conference on Fun with Algorithms
Year:
2012

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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.