Generalised acyclic edge colourings of graphs with large girth

The r-acyclic edge chromatic number of a graph G is the minimum number of colours required to colour the edges of G in such a way that adjacent edges receive different colours and every cycle C receives at least min{|C|,r} colours. We prove that for any integer r?4, the r-acyclic edge chromatic number of any graph G with maximum degree Δ and with girth at least 3(r-1)Δ is at most 6(r-1)Δ.     

算法的发现(IV)——论组合优化的特性清单

组合优化问题的定义［１］是定义１问题ＸＹＺ是指：对于每一个π（１）－集合Ｓ，从其诸π（２）－子集合中找出π（３）－（优）集合Ｓ＊．本文直接从它出发，§§２－５讨论诸π（ｉ）－集合（ｉ＝１，２，３）的某基本特性（ｐｒｏｐｅｒｔｙ），公理（ｐｏｓ－ｔｕｌａｔｅ），或者特殊情形（ｐａｒｔｉｃｕｌａｒｃａｓｅ）．列出了一个清单ＰＰＰ，叫做特性清单．它远非完善，但已经可以用来讨论不少问题．§６起简单地讨论若干个子清单，所对应的问题类，并讨论求解它们的一些方法．     

关于Tuza和Voigt的(Dm,m)-可选择性刻画定理

给出一个不属于Non-D的图,但该图却不是(Dm,m)-可选择的.这表明在Tuza Zs和Voigt M的Non-D定义和(Dm,m)-可选择图的特征化定理中存在一定的冲突.针对如上冲突,对Tuza Zs和Voigh M所给出的Non-D的定义,以及(Dm,m)-可选择图的特征化定理的证明进行了修正.     

Colouring random graphs

We discuss some results concerned with the behaviour of colouring algorithms on large random graphs.     

Implementing the ALGOL 68 heap

The implications of the heap, reference variables and global generators in ALGOL 68 are examined and some notes on possible implementation mechanisms are presented. In particular the use or simulation of hardware with segment addressing facilities is discussed.     

添加剂对不锈钢着色过程的影响

探讨了添加剂在不锈钢着色过程中的作用和影响，在特定条件下可使不锈钢成品获得满意的结果。     

GOSAT-2009 methane spectral line list in the 5550-6236 cm range

A methane spectral line list for the 5550-6236 cm⁻¹ range with the intensity cut off 4×10⁻²⁶ cm/molecule at 296 K is presented. The line list is based on new extensive measurements of methane spectral line parameters performed at different temperatures and pressures of methane and buffer gases N₂, O₂ and air. This spectral line list is prepared in HITRAN-2008 format and contains the following spectral line parameters of about 11,000 lines: position, intensity, energy for lower state (where possible), air-broadening and air-shifting coefficients, exponent of temperature dependence of air-broadening coefficient and self-broadening coefficient.     

On nice and injective-nice tournaments

One way of defining an oriented colouring of a directed graph $\overrightarrow{G}$ is as a homomorphism from $\overrightarrow{G}$ to a target directed graph $\overrightarrow{H}$, and an injective oriented colouring of $\overrightarrow{G}$ can be defined as a homomorphism from $\overrightarrow{G}$ to a target directed graph $\overrightarrow{H}$ such that no two in-neighbours of a vertex of $\overrightarrow{G}$ have the same image. Oriented colourings may be constructed using target directed graphs that are nice, as defined by Hell et al. (2001). We extend the work of Hell et al. by considering target graphs that are tournaments, characterizing nice tournaments, and proving that every nice tournament on $n$ vertices is $k$-nice for some $k\le n+2$. We also give a characterization of tournaments that are nice but not injective-nice.     

Coloring triangle‐free graphs with local list sizes

We prove two distinct and natural refinements of a recent breakthrough result of Molloy (and a follow‐up work of Bernshteyn) on the (list) chromatic number of triangle‐free graphs. In both our results, we permit the amount of color made available to vertices of lower degree to be accordingly lower. One result concerns list coloring and correspondence coloring, while the other concerns fractional coloring. Our proof of the second illustrates the use of the hard‐core model to prove a Johansson‐type result, which may be of independent interest.     

1-平面图的结构性质及其在无圈边染色上的应用

一个图称为是1-平面的如果它可以画在一个平面上使得它的每条边最多交叉另外一条边.本文描述了任意1-平面图中小于等于7度点之邻域的局部结构,解决了由Fabrici和Madaras提出的两个关于1-平面图图类中轻图存在性的问题,证明了每个最大度是△的1-平面图G是无圈列表max{2△-2,△+83}-边可选的.