Knight's Tour Revisited Revisited

 

Title: Knight's Tour Revisited Revisited
Author: Lukas Koller (lukas /dot/ koller /at/ tum /dot/ de)
Submission date: 2022-01-04
Abstract: This is a formalization of the article Knight's Tour Revisited by Cull and De Curtins where they prove the existence of a Knight's path for arbitrary n × m-boards with min(n,m) ≥ 5. If n · m is even, then there exists a Knight's circuit. A Knight's Path is a sequence of moves of a Knight on a chessboard s.t. the Knight visits every square of a chessboard exactly once. Finding a Knight's path is a an instance of the Hamiltonian path problem. A Knight's circuit is a Knight's path, where additionally the Knight can move from the last square to the first square of the path, forming a loop. During the formalization two mistakes in the original proof were discovered. These mistakes are corrected in this formalization.
BibTeX:
@article{Knights_Tour-AFP,
  author  = {Lukas Koller},
  title   = {Knight's Tour Revisited Revisited},
  journal = {Archive of Formal Proofs},
  month   = jan,
  year    = 2022,
  note    = {\url{https://isa-afp.org/entries/Knights_Tour.html},
            Formal proof development},
  ISSN    = {2150-914x},
}
License: BSD License
Status: [ok] This is a development version of this entry. It might change over time and is not stable. Please refer to release versions for citations.