 used the Hajós construction to generate an infinite set of 4-critical polyhedral graphs, each having more than twice as many edges as vertices.Similarly, used the construction, starting with the Grötzsch graph, to generate many 4-critical triangle-free graphs, which they showed to be difficult to color using traditional backtracking algorithms.In polyhedral combinatorics, used the Hajós construction to generate facets of the stable set polytope.