On the Treewidth of Hanoi Graphs

Authors David Eppstein, Daniel Frishberg , William Maxwell

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Author Details

David Eppstein
  • University of California, Irvine, CA, USA
Daniel Frishberg
  • University of California, Irvine, CA, USA
William Maxwell
  • Oregon State University, Corvallis, OR, USA


Some of the results in the section on three-peg Hanoi graphs were previously announced on a web forum [Eppstein, 2016].

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David Eppstein, Daniel Frishberg, and William Maxwell. On the Treewidth of Hanoi Graphs. In 10th International Conference on Fun with Algorithms (FUN 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 157, pp. 13:1-13:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph theory
  • Hanoi graph
  • Treewidth
  • Graph separators
  • Kneser graph
  • Vertex expansion
  • Haven
  • Tensor product


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