On minimally circular-imperfect graphs Original Research Article

A circular-perfect graph is a graph of which each induced subgraph has the same circular chromatic number as its circular clique number. In this paper, (1) we prove a lower bound on the order of minimally circular-imperfect graphs, and characterize those that attain the bound; (2) we prove that if G is a claw-free minimally circular-imperfect graph such that image for some image, then image for an integer k; and (3) we also characterize all minimally circular-imperfect line graphs.