This paper studies the on-line choice number of complete multipartite graphs with independence number m. We give a unified strategy for every prescribed m.Our main result leads to several interesting consequences comparable to known results. (1) If (Formula Presented)where kp denotes the number of parts of cardinality p, then G is on-line chromatic-choosable. (2) If (Formula Presented)then G is on-line chromatic-choosable. (3) The on-line choice number of regular complete multipartite graphs Km*k is at most k for (Formula Presented).
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