Radius versus diameter in cocomparability and intersection graphs Original Research Article

Whereas in general graphs the only connection between radius and diameter can be expressed by the inequality r(G)⩽diam(G)⩽2r(G), in this paper it is shown that much sharper inequalities of type 2r(G)-diam(G)⩽a are valid inside the classes of cocomparability graphs and trapezoid graphs, with constants a = 3,2. For circular-arc graphs and proper circular-arc graphs we obtain diam(G) - r(G)⩽b, with constants b=2,1.