1 research outputs found
The Resolution of Keller's Conjecture
We consider three graphs, , , and , related to
Keller's conjecture in dimension 7. The conjecture is false for this dimension
if and only if at least one of the graphs contains a clique of size . We present an automated method to solve this conjecture by encoding the
existence of such a clique as a propositional formula. We apply satisfiability
solving combined with symmetry-breaking techniques to determine that no such
clique exists. This result implies that every unit cube tiling of
contains a facesharing pair of cubes. Since a faceshare-free
unit cube tiling of exists (which we also verify), this
completely resolves Keller's conjecture.Comment: 25 pages, 9 figures, 3 tables; IJCAR 202