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

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 $n\in \{12,13\}$.