ON THE CROSSING NUMBER OF THE COMPLETE TRIPARTITE GRAPH K1,8,n

作     者：黄元秋 赵霆雷 

作者机构：Department of Mathematics Hunan Normal University Changsha 410081 China 

出 版 物：《数学物理学报》 (Acta Mathematica Scientia)

年 卷 期：2006年第S1期

页      面：1115-1122页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

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) 

主　　题：Graphs Drawing Crossing number Complete tripartite graph Complete tripartite graph. 

摘      要：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].