Latin Squares with Graph Properties

ABSTRACT. In a Latin square of size n every number from 1 to n occurs exactly once in every row and every column. Two neighbors (straight or diagonal) in a Latin square are connected by an edge if their values differ at most 1. We investigate Latin squares for which this underlying graph has typical graph properties, like being connected, being a tree or being Hamiltonian. Searching for such Latin squares shows up combinatorial explosion. Nevertheless, by exploiting current SAT/SMT solving, we explicitly find instances for several variants, or prove that they do not exist.