Closed (a, a + 1)-Knight’s Tours on some Square Tubes

Authors

  • Kharinthip Boonprasit Department of Mathematics, Faculty of Science, Ramkhamhaeng University, Bangkok, Thailand
  • Adthasit Sinna Department of Mathematics, Faculty of Science, Ramkhamhaeng University, Bangkok, Thailand
  • Sirirat Singhun Department of Mathematics, Faculty of Science, Ramkhamhaeng University, Bangkok, Thailand

Keywords:

a closed (a, b)-knight’s tour, the ringboard of width r, the (m, n, k, r)-rectangular tube

Abstract

In this article, we present sufficient and necessary conditions for the (2a + 1, 2a + 1, k, a)-tube where  is a positive integer and a equation {2, 3, 4} to have closed (a, a + 1)-knight’s tours. Moreover, closed (a, a + 1)-knight’s tours on the (2a + 1, 2a + 1, k, a)-tube are shown if it exists.

References

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Singhun S, Loykaew N, Boonklurb R and Srichote W. (2021) Closed knight’s tour problem on some (m, n, k, 1)-rectangular tubes Asian-European J of Math Vol14 No 6, 17pages

Watkins J J (2004) Across the Board: The Mathematics of Chessboard Problems Princeton University Press, New Jersey

Wiitala HR (1996) The knight’s tour problem on boards with holes Res Exp Undergraduates Proc, 132-151

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Published

2025-12-31

Issue

Vol. 8 No. 3 (2025): September- December

Section

Original Articles

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