Which chessboards have a closed knight's tour within the rectangular prism?

7Citations
Citations of this article
6Readers
Mendeley users who have this article in their library.

Abstract

A closed knight's tour of a chessboard uses legal moves of the knight to visit every square exactly once and return to its starting position. In 1991 Schwenk completely classified the m × n rectangular chessboards that admit a closed knight's tour. In honor of the upcoming twentieth anniversary of the publication of Schwenk's paper, this article extends his result by classifying the i × j × k rectangular prisms that admit a closed knight's tour.

References Powered by Scopus

Which chessboards have a closed knight's tour within the Cube?

11Citations
N/AReaders
Get full text

Cited by Powered by Scopus

The closed knight tour problem in higher dimensions

6Citations
N/AReaders
Get full text

Closed knight's tour problem on some (m, n, k, 1)-rectangular tubes

1Citations
N/AReaders
Get full text

Tours of a generalized knight on rectangular chessboards

0Citations
N/AReaders
Get full text

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Cite

CITATION STYLE

APA

Demaio, J., & Mathew, B. (2011). Which chessboards have a closed knight’s tour within the rectangular prism? Electronic Journal of Combinatorics, 18(1), 1–14. https://doi.org/10.37236/495

Readers over time

‘14‘15‘16‘1700.511.52

Readers' Seniority

Tooltip

PhD / Post grad / Masters / Doc 2

50%

Professor / Associate Prof. 1

25%

Lecturer / Post doc 1

25%

Readers' Discipline

Tooltip

Mathematics 3

50%

Agricultural and Biological Sciences 1

17%

Biochemistry, Genetics and Molecular Bi... 1

17%

Computer Science 1

17%

Save time finding and organizing research with Mendeley

Sign up for free
0