New Lower Bounds for Snake-in-the-Box in 10-, 11-, 12-, and 13-dimensional Hypercubes

The Snake-in-the-Box problem is the challenge of finding the longest possible induced path in the edge graph of an n-dimensional hypercube. Although the problem is unsolved in hypercubes of dimension 9 and above, research continues to refine lower and upper bounds on maximum possible path length. This paper presents snakes which establish by example new lower bounds of 376, 736, 1445, and 2854 in 10, 11, 12, and 13 dimensions, respectively, and describes the simple heuristics used in their discovery.