关于给定控制数的连通二部图的极大图的刻画
ON THE CHARACTERIZATION OF THE MAXIMAL CONNECTED BIPARTITE GRAPHS WITH GIVEN DOMINATION NUMBER

本文研究了给定控制数的连通二部图的极大图的结构问题. 利用分类讨论思想和数学归纳法, 刻画了控制数等于3 和大于等于4 这两类边数达到极值时的连通二部图. 本文所得结果可用于进一步研究给定全控制数的连通二部图的极大图问题.
In this paper, the structure of the maximal connected bipartite graphs with a given domination number are studied. Using classification method and mathematical induction, this paper will assume the domination number is 3 or equal or greater than 4, respectively, and characterize connected bipartite graphs with the maximal size.The main results can be used in the future for studying the maximal connected bipartite graphs with given total domination number