On the Crossing Number of the Complete Tripartite Graph
نویسنده
چکیده
Abstract: The well known Zarankiewicz’ conjecture is said that the crossing number of the complete bipartite graph Km,n (m ≤ n) is Z(m, n), where Z(m,n) = ⌊ m 2 ⌋⌊ 2 ⌋⌊ 2 ⌋ ⌊ 2 ⌋ (for any real number x, ⌊x⌋ denotes the maximal integer no more than x). Presently, Zarankiewicz’ conjecture is proved true only for the case m ≤ 6. In this article, the authors prove that if Zarankiewicz’ conjecture holds for m ≤ 9, then the crossing number of the complete tripartite graph K1,8,n is Z(9, n) + 12⌊ n 2 ⌋.
منابع مشابه
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