Lieb's square ice constant is a mathematical constant used in the field of combinatorics to quantify the number of Eulerian orientations of grid graphs.

[1] An n × n grid graph (with periodic boundary conditions and n ≥ 2) has n2 vertices and 2n2 edges; it is 4-regular, meaning that each vertex has exactly four neighbors.

Denote the number of Eulerian orientations of this graph by f(n).

[3] Some historical and physical background can be found in the article Ice-type model.

This graph theory-related article is a stub.