University of Cambridge > Talks.cam > Combinatorics Seminar > Generalised Knight Tours

Generalised Knight Tours

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

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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.

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