几类乘积图的均匀着色

考虑了几类乘积图的均匀着色数,证明了这几类乘积图可均匀k-着色(k≥2或3)。     

d-退化图松弛均匀着色的一个注记

松弛均匀着色是松弛着色的一类特殊情况,它要求任意两个色类的顶点数之差至多为1．d-退化图是指每个导出子图都存在度至多为d的顶点的图．证明了若顶点数位rt的d-退化图G的最大度至多为△,且K≥18d,n≥17△．则G存在均匀（k-1,1）着色．     

不含3-圈和4-圈的平面图的列表均匀染色

任意给定图G的一个k-一致列表L,若G是L-可染的,且满足每种颜色至多在「｜V（G）/k｜」个点上出现,则称G是k-均匀可选择的．若图G有一个正常k-顶点染色满足任两个色类中的顶点数至多相差1,则称G是k-均匀可染的．应用discharge方法讨论了不含3-圈和4-圈的平面图的结构,证明了对于不含3-圈和4-圈的平面图G,当k≥{max△（G）,6）时,G是k-均匀可选择的,同时G也是k-均匀可染的．     

Halin图的均匀染色

Ｈａｌｉｎ图是最小广东 小于３的３－连通平面图,且存在一个面,删除关联于该面的所有边后是一棵树。称图Ｇ的均匀Ｋ－可着色的,如Ｇ的顶点集Ｖ１、Ｖ２、…Ｖｋ,使｜｜Ｖｉ｜－｜Ｖｊ｜｜≤１（０≤ｉ〈ｊ≤ｋ）;称使图Ｇ的均匀ｋ－可着色的最小整数ｋ为Ｇ的均匀色数,记为Ｘｅ（Ｇ）。本文对非Ｋ４的Ｈａｌｉｎ图图证明了当△（Ｇ）≠４时,对任意的整数Ｋ≥「△（Ｇ）／２」＋１;当△（Ｇ）＝４时,对任意整数的Ｋ≥４,Ｇ     

有关满着色的一些结果

图G=(V,E)的一个正常k-着色实际上是将G的顶点划分为独立集,记为∏={V1,V2,…,Vk}.其中Vi,i=1,2,…,k,也称色类.对于任一色类Vi中的点v,如果它与其余色类中至少一个点相邻,则v被称为是满色的.如果在G的一个正常k-着色中,所有点都是满色的,则称这样的着色是满着色.如果一个图存在满着色,定义图的满着色数为使得图存在满着色的最小颜色数,记为χf(G).另外,记ψf(G)为使图存在满着色的最大颜色数.本文主要研究了有关满着色的一些性质,并给出一个满着色与完美图之间的结论.     

关于Sn＋Fn和Sn＋Wn的均匀全染色

对于图G的正常k-全染色f称为G（V,E）的k-均匀全染色,当且仅当任意2个色类中的元素总数至多相差1.χet（G）=min{k｜G有k-均匀全染色}称为图G的均匀全色数.利用均匀边染色的相关结论,讨论并得到了图Sn＋Fn和Sn＋Wn的均匀全色数.     

M(P_n)和M(C_n)的邻点可区别均匀全染色

如果图G的一个正常全染色满足任意两相邻顶点的色集不同,并且任意两种颜色所染元素数目相差不超过1,则称为图G的邻点可区别均匀全染色,其所用最少染色数称为图G的邻点可区别均匀全色数.本文根据图的结构关系,运用构造法确定了路和圈的Mycielski图的邻点可区别均匀全色数.由此验证了邻点可区别均匀全染色的猜想对于路和圈的Mycielski图也是正确的.     

一类Halin—图的均匀色数

对△（Ｇ）＝４的Ｈａｌｉｎ－图证明了｜Ｖ（Ｇ）｜≠０（ｍｏｄ３）时，对任意整数的ｋ≥「△（Ｇ）／２」＋１，Ｇ是可均为Ｋ－可着色的。从而证明了这类Ｈａｌｉｎ－图的均匀染色数的下界是「△（Ｇ）／２」＋１。     

关于图的点强全着色

图G(V,E)的一正常k-全着色σ称为G(V,E)的一个k-点强全着色,当且仅当ν∈V(G),N[ν]中的元素着不同颜色,其中N[ν]={u|νu∈E(G)}∪{ν}。并且χνsT(G)=min{k|存在G的一个k-点强全着色}称为G(V,E)的点强全色数。本文得到了一些特殊图的点强全色数χνsT(G),并提出猜想:对于简单图G,有k(G)≤χνsT(G)≤k(G) 1,这里k(G)是文中给出的一个新的参数。     

周期着色在3类集上的应用

设P是所有素数的集合，D是P的任意一个子集，素距离图Z(D)是这样一个图：其顶点集是所有整数，当且仅当|x-y|∈D时，点x利y之间有边相连．文[1]已证明Z(D)的色数最多是4，即X(D)≤4．因而可按照Z(D)的分类把P的所有子集D分为四类．本文用周期着色得到了若干D是3类集的充分条件．     

Proofs for some known results of equitable coloring

A graph is equitably k-colorable if its vertices can be partitioned into k independent sets of as near equal sizes as possible. In this paper, we give new methods to prove some known results of equitable coloring of complete r-partite Graphs.     

具有最少可能边数的唯一k-可染色图的构造

Abstract It was shown that a uniquely vertex k-colorable graph of order n has minimum size n（k - 1） - （^k2）, and a uniquely vertex 3-colorable extremal graph with the minimum degree 3 can be constructed. In this note, we construct-an infinite familyof uniquely vertex k-colorable graphs of the order n, the size n（k - 1） - （^k2） and the minimum degree k by using a recursion method.     

论课程资源的公平分配

公平分配直接攸关实质公平,如何将有限的课程资源在学生间进行公平的分配,既是学生应得课程资源的结构问题,也是课程实质公平的核心内容之一。     

论教育改革代价的公正分配

教育改革代价的付出具有一定的必然性,其分配是一个不容回避的问题.教育公正是基本的社会公正之一,因而教育改革代价的公正分配必然关系到社会公正问题.教育改革代价的分配不同于物质财富的分配,有其自身的分配逻辑.对教育改革所产生的必然代价应进行合理、公正的分配,其分配应遵循差别原则、应得原则和补偿原则.     

The implications of an across-the-board salary increase

The implications of an across-the-board salary increase for selected outcomes are assessed. While such an approach to employee compensation is easily administered, the results of this analysis suggest that such an approach has some long-run costs. Those perceiving themselves as high performers and as putting forth greater effort felt undercompensated. Those with feelings of being undercompensated, relative to those feeling equitably compensated, anticipated a reduction in their job performance during the coming year, and perceived a deterioration in the association between performance and compensation. Differences in intentions to search for alternative employment are statistically significant.     

Education with(out) distinction: beyond graduate attributes for Chinese international students

The recent explosion of Chinese students in Australian universities presents serious challenges for staff in higher education as we try to meet the conflicting demands of our positions. On one hand, we must offer diverse international students opportunity to compete equitably with their Australian counterparts and to receive an appropriate ‘Western’ education; on the other, we must work within the university's education policies which, ironically, have become increasingly homogenising. We here suggest that Confucian philosophy can offer us two-fold insight: first, into the ‘educability’ of international students and, second, into our roles as education providers. In this paper we present the philosophy, curriculum and outcomes of a 3rd-year Asian Studies course targeted exclusively to speakers of Chinese, in order to evaluate the importance of providing these students with fair and rigorous opportunities that are directly relevant to their educational aspirations. This course was specifically designed to meet the university's mandated ‘graduate attributes’ by developing students' command of written critique following ‘Western’ conventions of logical argument and without plagiarism. It is based on a theoretically transcultural ‘pedagogy of connection’ and, significantly, it is conducted bilingually in English and Chinese. Through a qualitative, constructivist analysis of this course, we argue the importance of dismantling the dominant, invisible, monolingual framing of Australian higher education in the strategic practice of course design, delivery and assessment so that prescribed Anglo-Celtic institutional goals can be realised equitably for international students.     

阅读能力的内涵与测试

阅读是获取语言知识直接，最有效的方法，阅读能力则是衡量掌握语言综合能力的一项重要标志，对于英语教师和测试工作来说，理解阅读能力的内涵及其与测试之间的关系，科学地，有效地测试学习的英语阅读能力，对于提高课堂教学的效率和学习的兴趣，公平，客观地衡量，检测教学效果是非常重要的。     

谈谈学生评价中的偏差现象

学生评价是促进学生全面发展和谐发展的重要手段。由于受到功利主义思想、晕轮、刻板效应、情感情绪等诸多因素的影响,教师对学生的评价常常出现偏差。为了避免这种偏差,教师应当提高教师精神境界,树立正确的学生观,客观公平评价学生,学习和掌握基本的心理学知识。