Links

Updated January 2023 (last revision was June 2012)

A large number of links previously here disappeared into the ether.
It is unfortunate that websites often show no dates of publication or last revision.
Let me know of other links that you think should be included.
I will try to keep it up to date. Use right click if required to open in separate tag or window.


Sections on this page: — Historical Information in date orderRecent Articles (since 2000) in alphabetical order

éHistorical Information in date order

8th century: Celtic Art The St Madoes Stone, photo, Perth Museum.

1315 Moschopoulos P. G. Brown The Magic Squares of Manuel Moschopoulos.

1741 Leonhard Euler Euler Archive E53 Solutio Problematis ad Geometrium Situs Pertinensis. (1741). [The Konigsburg Bridges Problem etc.]
1766 Euler Archive E309 Solution d'une question curieuse que ne paroit soumise a aucune analyse. (presented 1759). [The first mathematical paper on Knight's Tours].

1782 Laisement Essai sur les Problèmes de Situation... (Rouen, chez Jean Racine, 1782, 74 pages) by Denis Ballière de Laisement (1729-1800).


1804 Mauvillon Chessgames.com Friedrich Wilhelm von Mauvillon (1774-1851), a Dutch army officer who played the first known correspondence chess games with a friend in Breda while stationed at the Hague in 1804 and published them in 1827:
Anweisung zur Erlernung des Schachspiels. The tours are in Chapter 6 §12 Rösselsprung p.239-240 and Tab X Figs 1-5.

1823 Warnsdorf Warnsdorf 1823 in Google Books - Princeton University Library copy - but lacks diagrams.

1827 Automaton Franklin Journal and American Mechanics' Magazine 1827 "Observations upon the Automaton Chess Player, now exhibiting in this city by Mr Maelzel, and upon various Automata and Androides" vol.3 p.125-131. "The Knight's move in the Game of Chess" p.132-134.

1837 Addison G. A. Addison Indian Reminiscences 1837.

1840: Roget Philosophical Magazine Archive Many issues of The Philosophical Magazine (Taylor & Francis) back to 1798 are listed, but regrettably these do not include the volumes for 1840-1848 that contain the knight's tour work of Peter Mark Roget, William Beverley and George Walker.

1842 Perenyi Mnemonik des schachspieles by L. Perenyi, in Google Books, also (other editions?):
Peranyi 1842.
Perenyi 1842.

1842 Kafer Vollständige Anweisung zum Schachspiele (Graz 1842) by Victor Käfer (b.1799). "Vom Rosselsprunge", vol.4 p.191-193. This Google Books text lacks diagrams which were on a fold-out sheet.

1844 Brede Almanach für Freunde vom Schachspiel (Altona 1844) by Ferdinand Julius Brede (1800-1849). 24 tours in diagram form at the end of the book.

1849 Poirson-Prugneaux Introduction Pratique du Jeu des Echecs by Q. Poirson-Prugneaux 1849.

1850 Stein Manuel de l'Amateur de Jeu des Echecs (Delarue, Paris, c.1850 p.132-138) by Elias Stein (1748-1812). "Problême dont la solution a été donnée par M. Euler". The first two Euler (1759) tours and the Moivre (1725) tour.

1852 Mysore Maharajas of Mysore in Wikipedia, and Krishnaraja Wadiyar III Krisharaj Wadiar (1794-1868) the Rajah of Mysore, biographic note.

1859 Mann 120 neue Rösselsprunge (Nürnberg 1859, by J. Mann jr.

1859 Knight English Cyclopedia, Arts and Sciences (London vol.2 1859) by Charles Knight. Cites Roget (1840) and gives a tour from Tomlinson (1845).

1862 Jaenisch Traité des Applications de l'Analyse Mathématique au Jeu des Echecs (3 volumes St Petersburg 1862-3)
by Carl Friedrich Andreyevich Jaenisch (1813-1872), in Google Books.

1864 Haldeman Tours of a Chess Knight (E. H. Butler & Co Phladelphia 1864) by Samuel Stehman Haldeman (1812 - 1880).

1870 Frost Biography of Andrew Hollingworth Frost (1819-1907) by Christian Boyer (after 1967).

1874 Linde Geschichte un Litteratur des Schachspiels by Antonius van der Linde (1833-1897), in Google Books.

Puzzle Columns in French Newspapers 1876 - 1885.
M. A. Feisthamel edited puzzle column in Le Siecle 1876-1885.
Le Siècle about the French newspaper 1836-1932, in Wikipedia.
Le Siècle on line archive of all editions.

1881 Lucas Portrait and Biobibliography of Edouard Lucas (1842-1891), flag links lead to French and English text. Articles on knight tours in various publications.

1884 Miller Mathematical Questions and their Solutions from the Educational Times edited by W. J. C. Miller 1884.

1894 Wolf Astronomische Mitteilungen {Astronomy Information} by Rudolph Wolf (1816-1893) "Studie über den Rösselsprung" §83 p.74-77 (1894). This knight's tour article is between passages about sun-spots! The tour shown is the one Euler sent to Goldbach 1757.

1895 Maczuski Heritage des Echecs Francais This is an account of a chess exhibition put on by A. L. Maczuski and Stella Goulieux in Amiens in 1895.


1900 Ligondes Ligondès family genealogy. Also: Disnematin family gives dates of (Vicomte) Raoul de Ligondès, (1847-1917) who is probably the Ligondes who wrote as "Palamede".

1919 Collini Notes & Queries 1919, with Collini style tour by John W. Brown.

1930-1951 Dawson Problemist Fairy Chess Supplement & Fairy Chess Review Volumes 1-7, edited by T. R. Dawson, on the British Chess Problem Society website.

1991 Murray Katherine Maud Elisabeth Murray (1909-1998) Biographical note about daughter of H.J.R. Murray, whom I met in 1991.


éRecent Articles (since 2000) listed alphabetically by authors or website

Archimedes' Laboratory (G. A. Sarcione & M-J. Waeber). Archimedes Lab Knight's Tour Puzzles and Graphs on shaped boards, apparently based on Japanese sources.

Eric Bainville. euler.free.fr Non-crossing paths. Diagrams of all solutions 3x3 to 9x9.

John D. Beasley John and Sue Beasley website J. D. Beasley 'Two notes on magic knight's tours' in Other Games and Puzzles section. March 2012.

Stefan Behnel. behnel.de What the chess knight is doing.

Nikolai Ivanov Beluhov. arxiv.org On Crosspatch Knight's Tours. 7-page PDF. (13 October 2013).
Also arxiv.org The Second Leaper Theorem (27 June 2017).
Also arxiv.org A Proof of Willcocks's Conjecture (19 August 2017).
Also arxiv.org The Flexibility and Rigidity of Leaper Frameworks (10 November 2019).
Also arxiv.org Leaper Tours (27 April 2021).
Also arxiv.org Induction on Descent in Leaper Graphs (20 September 2021).
Also arxiv.org Snake Paths in King and Knight Graphs (3 January 2023).

Alex Black/Chernov. alex-black.ru Npn-inersecting paths. Table of best results including rectangular boards, also other leapers.

Ron Brown. artistwebsites.com Art, some based on knight tours.

Andrew Buchanan and Hiroaki Maeshima. drive.google.com Riding on the Plane (2023). Also in Hopper magazine.

Hector Cancela & Ernesto Mordecki. arxiv.org Counting Knight's Tours through the Randomized Warnsdorff rule (2006).

Chess Archaeology. Chess Archaeology lists back issues of Chess Journals online. Includes Sissa.

Edward D. Collins. edcollins.com home page. with links to: A Knight's Tour. In fact five tours the last being Beverley's (misattributed to Euler).

Michael Creighton. Quixote2013 Art based on knight tours.

Gary Darby. delphiforfu.org Knight's tour program.

Yann Denef. Two-Knight Magic Tours on 8x8 Board by Yann Denef. Includes all types of link moves.

V. P. Desai. tripod.com. About realisations of the knight tour using java programming.

Joshua Erde and B. and S. Golenia arxiv.org The closed knight tour problem in higher dimensions. (20 April 2012).

The Gams and Puzzles Journal 2001-2006 The Games and Puzzles Journal These issues #19 - #45 include many tour results. Note particularly: the 10×10 Semimagic tour by Tom Marlow, and the two new 8×8 magic knight tours by Tim Roberts, in #25 (January-February 2003), and the four 12×12 diagonally magic tours by Awani Kumar in #26 (March-April 2003).

Donald P. Irwin. atari Creative computing.

G. P. Jelliss Jeepyjay Diary (2011): Magic knight tour on 12x14 board.

Nina Kamcev arxiv.org Generalised Knight's Tours (7 February 2014).

Mark R. Keen. markkeen.com The Knight's Tour - Large site on graph theory.

Mike Keith. Cadaeic - Mike Keith's website.
Prime Tour - Figured tour with primes in line with a fixed square.
Wordways An article by Mike Keith on "Knight's Tour Letter Squares", available as PDF download.

Graham Kendall. the conversation.com How to get ants to solve a chess problem.

Donald E. Knuth: stanford.edu Selected Papers on Fun and Games.
Also arxiv.org Leaper Graphs (1 Nov 1994).

Vaclav Kotesovec. kotesovec.cz Fairy Chess articles with many links. In particular: PDF: Dual Free Leaper and Hopper Tours. In Czech with English commentary.

Awani Kumar. arxiv.org 3, 4, 5D magic tours!
Also: arxiv.org Noncrossing paths in 3D.
See also Games and Puzzles Journal 2003.

Kuo-Chun Lee and Yoshiyasu Takefuji. ieee.org Abstract: Finding knight's tours on an M×N chessboard with O(MN) Hysteresis McCulloch-Pitts neurons.

Joe Leslie-Hurd. cl.cam.ac.uk Links to a page about large tours.

M. Löbbing and I. Wegener. Combinatorics Attempt to enumerate the tours on the 8x8 board (1996). Incorrect. Later revised. Link to McKay paper.

Hugues Mackay. See Magic Tour News.

Magic Tour News updates Includes (now some way down the page) "Computing Magic Knight Tours" 2003, by Hugues Mackay, J-C. Meyrignac and G. Stertenbrink. The complete enumeration of 8x8 magic knight tours.

Samuel L. Marateck. arxiv.org How good is the Warnsdorff's [sic] knight's tour heuristic? (2008).

T. W. Marlow. See Games and Puzzles Journal 2003.

Brendan D. McKay. PDF Knight's Tours of an 8x8 Chessboard Number found differs from Lobbing and Wegener paper.

Zvi Mendlowitz. kotesovec.cz Geometrically longest king's closed tour on a 8x8 chessboard.

Jean-Charles Meyrignac. Non-Crossing Knight Tours
Also Formula 4.n^2 + 4.n formula.
Also see Magic Tour News.

Ed. Pegg. mathpuzzle.com Leaper tours page.

Ivars Peterson. mathtourist Model of knight cubic tour by Loren Larson.

Shariefuddin Pirzada and Ashay Dharwadker. dharwadker.org Applications of Graph Theory. Includes knight's tour example.

Tim S. Roberts. See Games and Puzzles Journal.

Elke Rehder. Historischer Überblick über die Entwicklung des Rösselsprunges A concise chronology of the knight's tour pronblem.
Includes Troupenas name and dates, Pongracz tour and portrait, Leipzig Illustriert tour, etc.

Colin Rose. tri.org.au Theoretical Research Institute - The Distribution of the Knight. Number of tours on boards of 32 or less cells.

Arnd Roth. library.wolfram.com The Problem of the Knight: A Fast and Simple Algorithm, 1999.

Science Direct sciencedirect.com Taming the knight's tour: minimising turns and crossings. By J. J. Besa et al, five authors (2 December 2021).

Guenter Stertenbrink. See Magic Tour News.

Ethan Y Tan and Guower Zhang arxiv.org Turns in Hamilton cycles of rectangular grids (20 July 2020).

Wikipedia. Knight's tour.
Knight's graph.
Springerproblem - German.
Longest uncrossed knight path..

Aale de Winkel. magichypercubes.com home page.
Catalogue of 8x8 magic knight tours.

Wolfram Mathworld. Knight Graph - The Knight's Tour page on Mathworld now redirects to this Knight Graph page.
Also: Magic Tour.
Also: Leaper Graph.


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