New Results on the Queens_n 2 Graph Coloring Problem

For the Queens_n ² graph coloring problems no chromatic numbers are available for n > 9 except where n is not a multiple of 2 or 3. In this paper we propose an exact algorithm that takes advantage of the particular structure of these graphs. The algorithm works on the independent sets of the graph rather than on the vertices to be colored. It combines branch and bound, for independent set assignment, with a clique based filtering procedure. A first experimentation of this approach provided the coloring number values ranging for n = 10 to n = 14.     

有向全图的幂敛指数和周期

设G是有向图,T(G)表示G的有向全图.本文得到了它们的幂敛指数k(G)和k(T)之间的关系:对任何有向图G,周期p(T(G))=1;当G是本原图时,k(T)≤k(G)+1,文中给出了取得k(G)+1的两类图;当G是无圈图时,k(T)=2k(G)-1,当G是有向圈时,k(T)=2|V(G)|-1,当G是强连通时得到了k(T)的一些估计.     

理想流体一维绝热稳定流动能量方程推导

对理想流体一维绝热稳定流动作了讨论．对一般理想流体(可压缩或不可压缩)，用两种方法推出了能量方程．在此基础上，讨论了流动可逆性及不同流体性质对流动参数的影响．     

θ*r,s,t-图与唯一2-列表染色图的特征化

如果一个图G存在一个k-列表安排使得G具有一个唯一列表染色,则称 G是唯一列表可染色图,简称UkLC图．我们称图G具有M(k)性质当且仅当G不 是UkLC图．本文在借鉴θr,s,t-图概念的基础上引入θr,s,t-图的定义,并证明:除了 r=s=t=2以外,θr,s,t-图都是U2LC图．利用如上结果我们给出M．Mahdian and E．S．Mahmoodian对U2LC图所作特征化的一个简单证明．     

反超图的笛卡儿积的上色数

讨论反超图的笛卡儿积的着色理论 ,求出了满足一定条件的反超图的笛卡儿积的上色数 .     

基于单通道反射型电光调制器实现不同路光同时调制的方法

提出了一种利用单通道反射型聚合物电光调制器同时调制不同路光的方法。衰减全反射结构的电光调制器,其每一个衰减全反射(ATR)峰的位置分别对应于一个导波共振模式。实验系统中利用衰减全反射导膜峰作为调制通道,使其每一路光路的入射角分别对应于不同导波共振模式的工作角,就可以实现利用单通道的电光调制器同时调制不同路光。提出了三种实现两路光同时调制的模式,并给出了三种模式的调制结果。结果表明,作为调制通道的导模阶数越低,调制效率越高。在832 nm光波波长下,采用最低阶导模进行调制时可以获得42.9%的调制效率。     

用分光光度法测定蜂胶超临界CO2萃取物中总黄酮含量

利用碱性条件下黄酮与Al3 生成粉红色络合物在可见光区510 nm处有最大吸收的特性,以芦丁为标样,采用分光光度法测定蜂胶超临界CO2萃取物中总黄酮含量,并与HPLC标准方法测定结果进行比较,发现各平行样的测定结果基本一致,最大偏差为268.38 mg/100 g,最小偏差为52.77 mg/100 g.该法简便快捷,结果相对准确,可作为蜂胶超临界CO2萃取物中总黄酮含量快速评估的一种方法.     

Coloring mixed hypertrees

A mixed hypergraph is a triple (V,C,D) where V is its vertex set and C and D are families of subsets of V, called C-edges and D-edges, respectively. For a proper coloring, we require that each C-edge contains two vertices with the same color and each D-edge contains two vertices with different colors. The feasible set of a mixed hypergraph is the set of all k's for which there exists a proper coloring using exactly k colors. A hypergraph is a hypertree if there exists a tree such that the edges of the hypergraph induce connected subgraphs of the tree.We prove that feasible sets of mixed hypertrees are gap-free, i.e., intervals of integers, and we show that this is not true for precolored mixed hypertrees. The problem to decide whether a mixed hypertree can be colored by k colors is NP-complete in general; we investigate complexity of various restrictions of this problem and we characterize their complexity in most of the cases.     

具有唯一4度最大度点的图的全色数

一个图Ｇ的全色数χ_T（Ｇ）是使得Ｖ（Ｇ）∪Ｅ（Ｇ）中相邻或相关联元素均染不同颜色的最少颜色数．文中证明了，若图Ｇ只有唯一的一个４度最大度点，则χ_T（Ｇ）＝Δ（Ｇ）＋１．