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Can You Walk This? Eulerian Tours and IDEA Instructions (Media Exposition)

Authors Aaron T. Becker , Sándor P. Fekete , Matthias Konitzny , Sebastian Morr , Arne Schmidt

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LIPIcs.SoCG.2021.62.pdf
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Subject Classification

ACM Subject Classification
  • Mathematics of computing → Discrete mathematics
  • Applied computing → Education
Keywords
  • Eulerian tours
  • algorithms
  • education
  • IDEA instructions

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Abstract

We illustrate and animate the classic problem of deciding whether a given graph has an Eulerian path. Starting with a collection of instances of increasing difficulty, we present a set of pictorial instructions, and show how they can be used to solve all instances. These IDEA instructions ("A series of nonverbal algorithm assembly instructions") have proven to be both entertaining for experts and enlightening for novices. We (w)rap up with a song and dance to Euler’s original instance.

Cite As Get BibTex

Aaron T. Becker, Sándor P. Fekete, Matthias Konitzny, Sebastian Morr, and Arne Schmidt. Can You Walk This? Eulerian Tours and IDEA Instructions (Media Exposition). In 37th International Symposium on Computational Geometry (SoCG 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 189, pp. 62:1-62:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021) https://doi.org/10.4230/LIPIcs.SoCG.2021.62

Author Details

Aaron T. Becker
  • Cullen College of Engineering, University of Houston, TX, USA
Sándor P. Fekete
  • Department of Computer Science, TU Braunschweig, Germany
Matthias Konitzny
  • Department of Computer Science, TU Braunschweig, Germany
Sebastian Morr
  • Department of Computer Science, TU Braunschweig, Germany
Arne Schmidt
  • Department of Computer Science, TU Braunschweig, Germany

References

  1. Blanche Descartes. The expanding unicurse. In Frank Harari, editor, Proof Techniques in Graph Theory, page 25. Academic Press, 1969. Google Scholar
  2. Leonhard Euler. Solutio problematis ad geometriam situs pertinentis. Commentarii academiae scientiarum Petropolitanae, pages 128-140, 1741. Google Scholar
  3. Sándor P. Fekete and Sebastian Morr. IDEA instructions. https://idea-instructions.com, 2018.
  4. M Fleury. Deux problèmes de géometrie de situation. Journal de mathematiques éleméntaires, 2(2):257-261, 1883. Google Scholar
  5. Karen A Frenkel. An interview with the 1986 ACM Turing award recipients - John E. Hopcroft and Robert E. Tarjan. Communications of the ACM, 30(3):214-222, 1987. Google Scholar
  6. Carl Hierholzer and Chr Wiener. Über die Möglichkeit, einen Linienzug ohne Wiederholung und ohne Unterbrechung zu umfahren. Mathematische Annalen, 6(1):30-32, 1873. Google Scholar
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