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arXiv · 2103.15778

Properties of Hamiltonian Circuits in Rectangular Grids

Rüdiger Jehn
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Abstract

We present properties and invariants of Hamiltonian circuits in rectangular grids. It is proved that all circuits on a $2n \times 2n$ chessboard have at least $4n$ turns and at least $2n$ straights if $n$ is even and $2n+2$ straights if $n$ is odd. The minimum number of turns and straights are presented and proved for circuits on an $n \times (n+1)$ chessboard. For the general case of an $n \times m$ chessboard similar results are stated but not all proofs are given.

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Rüdiger Jehn. 2021-03-29. Properties of Hamiltonian Circuits in Rectangular Grids. https://arxiv.org/abs/2103.15778

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