2,3-可选的完全二部图的刻划

摘要

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 K3.7 , K8.2K1.n, K2.n (n ≥ 1 ) and Km.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.%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3-可选的完全二部图有一定帮助.