Game coloring the Cartesian product of graphs

This article proves the following result: Let G and G′ be graphs of orders n and n′, respectively. Let G^* be obtained from G by adding to each vertex a set of n′ degree 1 neighbors. If G^* has game coloring number m and G′ has acyclic chromatic number k, then the Cartesian product G□G′ has game chromatic number at most k(k + m ? 1). As a consequence, the Cartesian product of two forests has game chromatic number at most 10, and the Cartesian product of two planar graphs has game chromatic number at most 105. © 2008 Wiley Periodicals, Inc. J Graph Theory 59: 261–278, 2008     

横向数据中累加死亡率的估计-附脑血管病实例

本文用现时寿命表中计算平均寿命的基本假定,讨论估计横向数据的累加死亡率问题.本公式也适用于累加发病率及任何非医学领域中某种指标的累加发生率等问题.文中使用了一个脑血管病实例.     

Reverse Mathematics and Grundy colorings of graphs

The relationship of Grundy and chromatic numbers of graphs in the context of Reverse Mathematics is investi‐gated (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

哈密尔顿性和部分平方图的独立集

设G是一个图,G的部分平方图G*满足V(G*)=V(G),E(G*)=E(G)∪{uv:uv■E(G),且J(u,v)≠■},这里J(u,v)={w∈N(u)∩N(v):N(w)■N[u]∪N[v]}.利用插点方法,证明了如下结果:设G是k-连通图(k2),b是整数,0min {k,(2b-1+k)/2}(n(Y)-1),则G是哈密尔顿图.同时给出图是1-哈密尔顿的和哈密尔顿连通的相关结果.     

Discrimination of cyclic peptide diastereomers by electrospray ionization tandem mass spectrometry

In this research, the characteristic ions' abundance ratio between two isomers A and B in MS/MS mass spectra was defined as a parameter for discriminating diastereomers. Through this ratio, the discrimination of four pairs of cyclic peptide (CP) diastereomers was successfully achieved. Furthermore, in the analysis of diastereomers' mixtures, both calibration curve and calculational methods were substantiated to have high precision and accuracy. The average absolute errors of the two methods were 2.0 and 2.5% in the 48 measurements of 16 samples, respectively. This research provided a promising approach for the analysis of the CP diastereomers in the fields of asymmetrical synthesis, chiral natural products and structural biology by ESI‐MS/MS. Copyright © 2009 John Wiley & Sons, Ltd.     

Smaller planar triangle-free graphs that are not 3-list-colorable

In 1995, Voigt constructed a planar triangle-free graph that is not 3-list-colorable. It has 166 vertices. Gutner then constructed such a graph with 164 vertices. We present two more graphs with these properties. The first graph has 97 vertices and a failing list assignment using triples from a set of six colors, while the second has 109 vertices and a failing list assignment using triples from a set of five colors.     

P-twisted affine Lie algebra and its realizations by twisted vertex operators

In this paper, we define a P-twisted affine Lie algebra, and construct its realizations by twisted vertex operators.     

An ant-based algorithm for coloring graphs

This paper presents an ant-based algorithm for the graph coloring problem. An important difference that distinguishes this algorithm from previous ant algorithms is the manner in which ants are used in the algorithm. Unlike previous ant algorithms where each ant colors the entire graph, each ant in this algorithm colors just a portion of the graph using only local information. These individual coloring actions by the ants form a coloring of the graph. Even with the lack of pheromone laying capacity by the ants, the algorithm performed well on a set of 119 benchmark graphs. Furthermore, the algorithm produced very consistent results, having very small standard deviations over 50 runs of each graph tested.     

图K(r,2)的邻强边色数

本文给出了每部有2个点的完全r-部图(r≥2)的邻强边色数.