几类循环图的分数染色数

通过构造几类图的最大独立集,给出了它们的分数染色数的下界;再通过构造具有该下界值的分数染色,给出了这几类循环图的分数染色数的上界,于是就确定了它们的分数染色数.     

郑玄《尚书》训诂的谶纬化

郑玄是汉学的总结性人物,其《尚书》训诂,是东汉《尚书》学之代表。郑玄《尚书》训诂,融古文、今文、谶纬于一体,是两汉《尚书》学谶纬化范围扩大的最好例证。通过郑玄,我们可以知道,古今文《尚书》学的对立并不妨碍双方对谶纬的吸收,谶纬在郑玄手中变成整合古今文《尚书》学的桥梁。     

Inapproximability and approximability of maximal tree routing and coloring

Let G be a undirected connected graph. Given g groups each being a subset of V(G) and a number of colors, we consider how to find a subgroup of subsets such that there exists a tree interconnecting all vertices in each subset and all trees can be colored properly with given colors (no two trees sharing a common edge receive the same color); the objective is to maximize the number of subsets in the subgroup. This problem arises from the application of multicast communication in all optical networks. In this paper, we first obtain an explicit lower bound on the approximability of this problem and prove Ω(g^1−ε)-inapproximability even when G is a mesh. We then propose a simple greedy algorithm that achieves performance ratio O√|E(G)|, which matches the theoretical bounds. Supported in part by the NSF of China under Grant No. 70221001 and 60373012.     

轮和完全等二部图联图的若干染色问题

图的染色理论是图论的一个重要分支。本文使用分析的方法得到了轮和完全等二部图联图的全色数、均匀全色数和邻点可区别边色数。     

The Independence Number of Graphs with a Forbidden Cycle and Ramsey Numbers

Let k 5 be a fixed integer and let m = (k – 1)/2. It is shown that the independence number of a C _k-free graph is at least c ₁[ d(v)^{1/(m – 1)}]^{(m – 1)/m} and that, for odd k, the Ramsey number r(C _k, K _n) is at most c ₂(n ^{m + 1}/log n)^1/m , where c ₁ = c ₁(m) > 0 and c ₂ = c ₂(m) > 0.     

An immune algorithm with stochastic aging and kullback entropy for the chromatic number problem

We present a new Immune Algorithm, IMMALG, that incorporates a Stochastic Aging operator and a simple local search procedure to improve the overall performances in tackling the chromatic number problem (CNP) instances. We characterize the algorithm and set its parameters in terms of Kullback Entropy. Experiments will show that the IA we propose is very competitive with the state-of-art evolutionary algorithms.     

On edge orienting methods for graph coloring

We consider the problem of orienting the edges of a graph so that the length of a longest path in the resulting digraph is minimum. As shown by Gallai, Roy and Vitaver, this edge orienting problem is equivalent to finding the chromatic number of a graph. We study various properties of edge orienting methods in the context of local search for graph coloring. We then exploit these properties to derive four tabu search algorithms, each based on a different neighborhood. We compare these algorithms numerically to determine which are the most promising and to give potential research directions.     

阳戏“三圣”信仰谫论

阳戏＂三圣＂指川主、土主、药王,他们是阳戏类型的标志。清吉镇宅、降福还愿是阳戏＂三圣＂信仰的宗旨。＂三圣＂由世间＂人＂向天上＂神＂的演化过程,浸润神秘性,并呈多样化的特点。文章采用文献阅读和田野调查结合的方法,对此问题进行探讨。     

论郭璞游仙诗中的忧患意识

郭璞是两晋时期著名的文学家和杰出的训诂学家。受政治环境和文化思潮的影响，他创作了多首游仙诗以表达自己寄情仙境、向往自由的心绪，这也成为他显著的外相特征。而事实上，在其游仙诗中却蕴含着深厚的忧患意识，包括对国家命运的忧思，对黎民苦难的忧戚，对时光流逝、生命短暂、壮志难酬的忧伤感慨。     

Proof of Toft's Conjecture: Every Graph Containing No Fully Odd K4 is 3-Colorable

A fully odd K₄ is a subdivision of K₄ such that each of the six edges of the K₄ is subdivided into a path of odd length. In 1974, Toft conjectured that every graph containing no fully odd K₄ can be vertex-colored with three colors. The purpose of this paper is to prove Toft's conjecture.