Nullhomotopic and Generating Knight’s Tours on Non-Orientable Surfaces

Authors

  • Bradley Forrest Stockton University
  • Zachary Lague New York University

DOI:

https://doi.org/10.46787/pump.v7i0.4231

Keywords:

knight's tour; non-orientable surfaces; fundamental groups

Abstract

We investigate closed knight’s tours on Möbius strip and Klein bottle chess boards. In particular, we characterize the board dimensions that admit tours that are nullhomotopic and the board dimensions that admit tours that realize generators of the fundamental groups of each of the surfaces.

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Published

2024-08-25

How to Cite

Forrest, B., & Lague, Z. (2024). Nullhomotopic and Generating Knight’s Tours on Non-Orientable Surfaces. The PUMP Journal of Undergraduate Research, 7, 157–185. https://doi.org/10.46787/pump.v7i0.4231

Issue

Vol. 7 (2024): PUMP Journal of Undergraduate Research

Section

Articles

License

Copyright (c) 2024 Bradley Forrest, Zachary Lague

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This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

The author(s) will retain the copyright, but by submitting the article agree to grant permission to the PUMP Journal of Undergraduate Research to publish, distribute, and archive the article. The author(s) will acknowledge prior publication in the PUMP Journal of Undergraduate Research for all future uses of the article or parts of it.