Year: 2020
Type: preprint
Abstract: For a Hamilton cycle in a rectangular $m \times n$ grid, what is the greatest number of turns that can occur? We give the exact answer in several cases and an answer up to an additive error of $2$ in all other cases. In particular, we give a new proof of the result of Beluhov for the case of a square $n \times n$ grid. Our main method is a surprising link between the problem of 'greatest number of turns' and the problem of 'least number of turns'.
Source: arXiv (Cornell University)
Authors: Tan, Ethan Y., Zhang, Guowen
Institution: University of Cambridge
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3043022399