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] [(m-1)/2] [n/2] [(n-1)/2](for and real number x, [x] denotes the...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] [(m-1)/2] [n/2] [(n-1)/2](for and real number x, [x] denotes the maximal integer no more than x). Presently, Zarankiewicz' conjecture is proved true only for the case m≤G. 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].展开更多
基金This work is supported by the Key Project of the Education Department of Hunan Province of China (05A037)by Scientific Research Fund of Hunan Provincial Education Department (06C515).
文摘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] [(m-1)/2] [n/2] [(n-1)/2](for and real number x, [x] denotes the maximal integer no more than x). Presently, Zarankiewicz' conjecture is proved true only for the case m≤G. 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].
