Circular complete graphs, circular clique number and circular perfect graphs

Suppose p > = 2q and (p, q) = 1. The circular complete graph K_{p/q} has vertex set { 0, 1, ..., p-1 }, in which i   and j   are adjacent if and only if  q <=  | i - j |  <=  p-q.

If q = 1, then K_{p/1} is the same as K_p.

The circular clique number omega_c(G) of a graph G is defined as

omega_c(G) = max { p/q : K_{p/q} admits a homomorphism to G }.

A graph G is called circular perfect if for every induced subgraph H of G,  chi_c(H)  = omega_c(H).