A proper circular-arc graph is a graph that has an intersection model formed by a family of overlapping arcs on some circle in which no arc contains another. A unit circular-arc graph is a graph that has an intersection model formed by a family of unit-length arcs on some circle. This paper gives structure theorems for proper circular-arc graphs and for unit circular-arc graphs. © 1974 North-Holland Publishing Company.
Tucker, A. (1974). Structure theorems for some circular-arc graphs. Discrete Mathematics, 7(1–2), 167–195. https://doi.org/10.1016/S0012-365X(74)80027-0