Abstract
The snake-in-the-box problem asks for the maximum length of a chordless path (also called snake) in the \(n\)-cube. A computer-aided approach for classifying long snakes in the \(n\)-cube is here developed. A recursive construction and isomorph rejection via canonical augmentation form the core of the approach. The snake-in-the box problem has earlier been solved for \(n\le 7\); that work is here extended by showing that the longest snake in the 8-cube has 98 edges.
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This work was supported in part by the Academy of Finland under Grant No. 132122, the GETA Graduate School, and the Nokia Foundation.
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Östergård, P.R.J., Pettersson, V.H. Exhaustive Search for Snake-in-the-Box Codes. Graphs and Combinatorics 31, 1019–1028 (2015). https://doi.org/10.1007/s00373-014-1423-3
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DOI: https://doi.org/10.1007/s00373-014-1423-3