Ohba´s Conjecture is True for Graphs K_6,3*t,2*(k-2t-4),1*(t+3)

A graph G is called chromatic-choosable if ch(G)=χ(G). Ohba´s conjecture states that every graph G with 2χ(G)+1 or fewer vertices is chromatic-choosable. In this paper we show that Ohba´s conjecture is true for complete multipartite graphs K_{6,3*t,2*(k-2t-4),1*(t+3)} and its all k-chromatic sub graphs for all integers t≥0 and k≥2t+4, that is, ch(K_{6,3*t,2*(k-2t-4),1*(t+3)})=k, which extends the result ch(K_{6,3*t,2*(k-6),1*4})=k given by Shen et al. [J. of Mathematical Research and Exposition, 27(2)(2007) 264-272].