[2,3]-可选的完全二部图的刻划(英文)  

Classification of [2,3]-Choosable Complete Bipartite Graphs

作　　者：胡琳[1] 王国平[1] 

机构地区：[1]新疆大学数学与系统科学学院,新疆乌鲁木齐830046

出　　处：《新疆大学学报（自然科学版）》2004年第4期361-365,共5页Journal of Xinjiang University(Natural Science Edition)

摘　　要：目前 ,所有 2 -可选的图在 [2 ]中已给出 ,但对 3-可选的图 ,即使是对 3-可选的二部图的分类仍未完成 .在[3]和 [4]中有一些相关结果 .事实上 ,这是一项困难的工作 .因此 ,在本文中 ,我们考虑了条件较弱一类图的分类问题 ,即对所有 [2 ,3]-可选的完全二部图进行了分类 .我们证明了 K3 ,7、K8,2 、 K1 ,n、K2 ,n和 Km,n( m + n≤ 9且当 n=4时 m≠ 5 )是所有的 [2 ,3]-可选的完全二部图 ,它对进一步刻划Although the 2-choosable graphs have been fully classified in [2], the 3-choosable graphs have not been classified yet, even if 3-choosable bipartite graphs. There are a few of results related it (see references [3] and [4]) and it seems difficult to completely classify the 3-choosable graphs. In this paper, we consider a weak problem, that is, to classify the [2,3]-choosable complete bipartite graphs. We prove that K_(3,7), K_(8,2) K_(1,n),K_(2,n)(n≥1) and K_(m,n) (m+n≤9 and m≠5 when n=4) are all [2,3]-choosable complete bipartite graphs, and thus the [2,3]-choosable complete bipartite graphs are completely characterized here, which, we consider, will be useful in the further research of the 3-choosable bipartite graphs.

关 键 词：完全二部图 刻划 证明 条件 分类问题 困难 帮助 事实 

分 类 号：N02[自然科学总论—科学技术哲学] O157.5[理学—数学]