On the treewidth of Hanoi graphs
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.
Cite
@article{arxiv.2005.00179,
title = {On the treewidth of Hanoi graphs},
author = {David Eppstein and Daniel Frishberg and William Maxwell},
journal= {arXiv preprint arXiv:2005.00179},
year = {2022}
}
Comments
- To be published in the Proceedings of the Tenth International Conference on Fun with Algorithms (FUN 2020). - 22 pages (including title page, bibliography, and appendix). - Five figures