GRAPHS THAT ADMIT 3-TO-1 OR 2-TO-1 MAPS ONTO THE CIRCLE

We give a complete and explicit characterization of the connected grap hs which admit a continuous 3-to-1 map onto the circle, and of the con nected graphs which admit a continuous 2-to-1 map onto the circle. Thi s generalizes earlier work of Heath and Hilton who considered the mapp ings of trees onto the circle.