New Snake-in-the-Box Records via Snakepit Surgery and Learned Construction

Excerpt

arXiv:2607.15270v3 Announce Type: cross Abstract: The snake-in-the-box problem asks for a longest induced path in the hypercube graph $Q_n$. We find a length-191 snake in dimension $n=9$, the lowest dimension where the maximum is unknown, improving the previous record of 190 that had stood for 14 years. We also establish new lower bounds in dimensions 10-13. To find these records, we introduce snakepits, collections of disjoint snakes, to expand the search space and open new routes between snake