Exhaustive Search for Snake-in-the-Box Codes

Abstract

The snake-in-the-box problem asks for the maximum length of a chordless path (also called snake) in the $$n$$n-cube. A computer-aided approach for classifying long snakes in the $$n$$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 $$n\le 7$$n≤7; that work is here extended by showing that the longest snake in the 8-cube has 98 edges.