The Thickness of Some Complete Bipartite and Tripartite Graphs  

作　　者：Si-wei HU Yi-chao CHEN 

机构地区：[1]Yali Peicui School,Changsha 410021,China [2]School of Mathematics,Suzhou University of Science and Technology,Suzhou 215009,China

出　　处：《Acta Mathematicae Applicatae Sinica》2024年第4期1001-1014,共14页应用数学学报（英文版）

基　　金：supported by the JSSCRC(Grant No.2021530);NNSFC under Grant No.12271392。

摘　　要：In this paper,we obtain the thickness for some complete k-partite graphs for k=2,3.We first compute the thickness of K_(n,n+8)by giving a planar decomposition of K_(4k-1,4k+7)for k≥3.Then,two planar decompositions for K_(1,g,g)(g-1)when g is even and for K^(1,g,1/2(g-1)2)when g is odd are obtained.Using a recursive construction,we also obtain the thickness for some complete tripartite graphs.The results here support the long-standing conjecture that the thickness of K_(m,n)is[mn/2(m+n-2)]for any positive integers m,n.

关 键 词：thickness complete bipartite graph complete tripartite graph planar decomposition 

分 类 号：O157.5[理学—数学]