In this article, we will determine the crossing number of the complete tripartite graphs K 1,3, n and K 2,3, n . Our proof depends on Kleitman's results for the complete bipartite graphs [D. J. Kleitman, The crossing number of K 5, n . J. Combinatorial Theory 9 (1970) 315‐323].
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Kouhei Asano (1986) studied this question.