New Bounds for the Snake-in-the-Box Problem

Abstract

The Snake-in-the-Box problem is that of finding a longest induced path in an $n$-dimensional hypercube. We prove new lower bounds for the values $n\in \{11,12,13\}$. The Coil-in-the-Box problem is that of finding a longest induced cycle in an $n$-dimensional hypercube. We prove new lower bounds for the values $n\in \{12,13\}$.

We improved six lower bounds from the previous version (two for snake-in-the-box and four for coil-in-the-box)

References in corpus (1)

• Constructing circuit codes by permuting initial sequences

Cited by in corpus (2)

• A New Method for Constructing Circuit Codes
• The Maximum Length and Isomorphism of Circuit Codes with Long Bit Runs