License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FUN.2021.13
URN: urn:nbn:de:0030-drops-127741
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12774/
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Eppstein, David ; Frishberg, Daniel ; Maxwell, William

On the Treewidth of Hanoi Graphs

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LIPIcs-FUN-2021-13.pdf (0.6 MB)

Abstract

The objective of the well-known Towers of Hanoi puzzle is to move a set of disks one at a time from one of a set of pegs to another, while keeping the disks sorted on each peg. We propose an adversarial variation in which the first player forbids a set of states in the puzzle, and the second player must then convert one randomly-selected state to another without passing through forbidden states. Analyzing this version raises the question of the treewidth of Hanoi graphs. We find this number exactly for three-peg puzzles and provide nearly-tight asymptotic bounds for larger numbers of pegs.

BibTeX - Entry

@InProceedings{eppstein_et_al:LIPIcs:2020:12774,
  author =	{David Eppstein and Daniel Frishberg and William Maxwell},
  title =	{{On the Treewidth of Hanoi Graphs}},
  booktitle =	{10th International Conference on Fun with Algorithms (FUN 2021)},
  pages =	{13:1--13:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-145-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{157},
  editor =	{Martin Farach-Colton and Giuseppe Prencipe and Ryuhei Uehara},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12774},
  URN =		{urn:nbn:de:0030-drops-127741},
  doi =		{10.4230/LIPIcs.FUN.2021.13},
  annote =	{Keywords: Hanoi graph, Treewidth, Graph separators, Kneser graph, Vertex expansion, Haven, Tensor product}
}

Keywords: Hanoi graph, Treewidth, Graph separators, Kneser graph, Vertex expansion, Haven, Tensor product
Collection: 10th International Conference on Fun with Algorithms (FUN 2021)
Issue Date: 2020
Date of publication: 16.09.2020

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