On T-set of T-colorings

Abstract: Let be the collection of sets T such that the greedy algorithm obtains the optimal T-span of for all , the collection of sets T such that is true for all graphs G. Many families in or have been discovered. We know that r-initial set and k multiple of s set are all in . Liu (T-colorings of graphs, Discrete Math. 10 (1992), 203–212) extended k multiple of s set by union with another set . In this paper, we continue to study the T-set in and , extending some T-sets by the similar way. [Copyright &y& Elsevier]