AbstractWe give a class of graphsGfor which there exists a homomorphism (= adjacency preserving map) fromV(G) toV(C), whereCis the shortest odd cycle inG, thereby extending a result of Albertson, Catlin, and Gibbons. Our class of graphs is characterized by the following property: For each odd subdivisionG′ ofGthere exists a homomorphic map fromV(G′) toV(C), whereC′ is the shortest odd cycle