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DOI: 10.4230/LIPIcs.FUN.2021.13
URN: urn:nbn:de:0030-drops-127741
URL: https://drops.dagstuhl.de/opus/volltexte/2020/12774/
Eppstein, David ; Frishberg, Daniel ; Maxwell, William
On the Treewidth of Hanoi Graphs
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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 | |
| Seminar: | 10th International Conference on Fun with Algorithms (FUN 2021) | |
| Issue date: | 2020 | |
| Date of publication: | 16.09.2020 |
