On T-set of T-colorings

Let G be the collection of sets T such that the greedy algorithm obtains the optimal T-span of Kn for all n⩾1, E the collection of sets T such that spT(G)=spT(Kχ(G)) is true for all graphs G. Many families in G or E have been discovered. We know that r-initial set and k multiple of s set are all in G∩E. Liu (T-colorings of graphs, Discrete Math. 10 (1992), 203-212) extended k multiple of s set by union with another set S′. In this paper, we continue to study the T-set in G and E, extending some T-sets by the similar way.