Geodesic
Generalised knight's tours
Nina Kamčev1
1University of Cambridge
The electronic journal of combinatorics, Tome 21 (2014) no. 1
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The problem of existence of closed knight's tours in $[n]^d$, where $[n]=\{0, 1, 2, \dots, n-1\}$, was recently solved by Erde, Golénia, and Golénia. They raised the same question for a generalised, $(a, b)$ knight, which is allowed to move along any two axes of $[n]^d$ by $a$ and $b$ unit lengths respectively.Given an even number $a$, we show that the $[n]^d$ grid admits an $(a, 1)$ knight's tour for sufficiently large even side length $n$.
DOI : 10.37236/3219
Classification : 05C45, 00A08
Mots-clés : Hamiltonian cycle, chessboard, knight

Nina Kamčev  1

1 University of Cambridge 
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     title = {Generalised knight's tours},
     journal = {The electronic journal of combinatorics},
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     number = {1},
     doi = {10.37236/3219},
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Nina Kamčev. Generalised knight's tours. The electronic journal of combinatorics, Tome 21 (2014) no. 1. doi: 10.37236/3219

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