University of Cambridge > > Combinatorics Seminar > Generalised Knight Tours

Generalised Knight Tours

Add to your list(s) Download to your calendar using vCal

  • UserNikolai Beluhov (Stara Zagora)
  • ClockThursday 28 November 2019, 14:30-15:30
  • HouseMR12.

If you have a question about this talk, please contact Andrew Thomason.

The classical knight tour problem extends naturally to generalised knights, which move by leaping $p$ units along one coordinate axis and $q$ units along the other. We require that $p + q$ is odd and that $p$ and $q$ are coprime, as otherwise the generalised knight cannot reach every cell. A well-known conjecture is that every generalised knight has a Hamiltonian cycle on some rectangular chessboard. We prove this conjecture. We also determine the smallest square chessboard with this property, whose side-length was first conjectured to be $2(p + q)$ by T. H. Willcocks in 1976.

This talk is part of the Combinatorics Seminar series.

Tell a friend about this talk:

This talk is included in these lists:

Note that ex-directory lists are not shown.


© 2006-2024, University of Cambridge. Contact Us | Help and Documentation | Privacy and Publicity