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http://hdl.handle.net/10012/5882
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| Title: | The Vulcan game of Kal-toh: Finding or making triconnected planar subgraphs |
| Authors: | Anderson, Terry David |
| Keywords: | triconnectivity
planarity
polyhedra
subgraphs |
| Approved Date: | 28-Apr-2011 |
| Date Submitted: | 21-Apr-2011 |
| Abstract: | In the game of Kal-toh depicted in the television series Star Trek: Voyager, players
attempt to create polyhedra by adding to a jumbled collection of metal rods. Inspired by
this fictional game, we formulate graph-theoretical questions about polyhedral (triconnected and planar) subgraphs in an on-line environment. The problem of determining the existence of a polyhedral subgraph within a graph G is shown to be NP-hard, 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. A two-player
formulation of Kal-toh is also explored, in which the first player to form a target subgraph is declared the winner. We show a polynomial-time solution for simple cases of this game but conjecture that the general problem is NP-hard. |
| Program: | Computer Science |
| Department: | School of Computer Science |
| Degree: | Master of Mathematics |
| URI: | http://hdl.handle.net/10012/5882 |
| Appears in Collections: | Electronic Theses and Dissertations (UW)
Faculty of Mathematics Theses and Dissertations
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