超图的2-可染色问题是超图染色的一个中心问题，图的控制集理论是目前图论研究的重要内容，也是运筹学选址问题的自然模型。本项目研究的核心内容包括：一、研究超图的2-可染色问题的一个重要的极值问题：一个至少拥有m(n)条边的 n-uniform 超图不是2-可染色的，则m(n)应为多少？本项目将围绕这个问题及相关问题进行研究，希望改进目前关于m(n)的上下界；二、利用超图2-可染色性研究中"slow recoloring"随机思想，结合半正定规划方法，研究图的各种染色问题；三、围绕Goddard和Henning在2009年关于配对控制数上界的猜想，考虑各种图类配对控制数上界估计和极图刻画，希望改进目前已知结果；四、考虑chordal graphs及其子图类上电力控制集问题算法复杂性、有效算法、近似算法等。

The 2-colorability of hypergraphs is a central issue in hypergraph coloring. The domination problem play an important role on graph theory,it is also a natural model for many locating problems in operations research.The core of this project include: First,we shall concentrate on the essential extremal problem on the 2-colorability of hypergraph: given a n-uniform hypergraph H, determine m(n), the minimum possible number of edges of H such that it is not 2-colorable.We hopt to improve the upper and lower bounds on m(n); Secondly,using "slow recoloring" random method in the research on the 2-colorability of hypergraph and semidefinite program,we shall consider some variations of graph coloring. Thirdly, around the conjecture of Goddard and Henning in 2009 on the upper bound of paired-domination number of graphs, we shall estimate the bounds on paired-domination numbers of the various classes of graphs and characterize extremal graphs. We hope to imporve the known results. At last, we shall consider the power domination problem on chordal graphs and its subclasses from algorithmic aspects.