Because "chains" could be tangled, Kempe's proof of a theorem about these objects was flawed.
These objects were studied by Heinrich Heesch, who developed the idea of "discharging." Because "chains" could be tangled, Kempe's proof of a theorem about these objects was flawed. Tait proved that theorem to be equivalent to the claim that no snarks are planar, and that theorem is a special case of the Hadwiger conjecture. One of these objects on a Klein bottle does not satisfy the conditions of the Heawood conjecture. Haken and Appel used a computer-aided proof that checks over nineteen-hundred reducible configurations of these objects in order to solve Guthrie's problem. For 10 points, name these objects from graph theory that can be properly colored with four hues.
These objects were studied by Heinrich Heesch, who developed the idea of "discharging."
maps [accept graphs before mentioned]