A tour of general Hanoi graphs

Daniel Berend, Liat Cohen, Omrit Filtser

פרסום מחקרי: פרסום בכתב עתמאמרביקורת עמיתים


The Tower of Hanoi puzzle has fascinated researchers in mathematics and theoretical computer science for over a hundred years. Many variants of the classical puzzle have been posed, such as allowing more than 3 pegs, and adding restrictions on the possible moves between the pegs. It is natural to view the pegs and allowed moves by means of a graph. The pegs are represented by the vertices of the graph, and the allowed moves by the edges. For each n, this graph yields a graph on the set of all legal configurations of n disks. Thus, the questions about the original puzzle may be reformulated as questions about connectivity and shortest paths in the graph of all configurations. Moreover, it was shown that classical Hanoi graphs are related to several interesting and useful structures such as the Sierpiński gasket and Gray codes, and thus several properties of these graphs were studied, including Hamiltonicity and planarity. In this paper we study these properties, and several others – chromatic number, clique number, and girth – for general Hanoi graphs.

שפה מקוריתאנגלית
מספר המאמר114289
עמודים (מ-עד)114289
מספר עמודים1
כתב עתTheoretical Computer Science
מזהי עצם דיגיטלי (DOIs)
סטטוס פרסוםפורסם - 1 פבר׳ 2024

הערה ביבליוגרפית

Publisher Copyright:
© 2023 Elsevier B.V.

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