平面图的(4,1)*-可选性

图G称为 (k ,d) 可选的 ,如果对满足条件L(v) =k(v∈V(G) )的任意指派L ,存在G的一个L着色使得G的每一个顶点至多有d个邻点与之着同色 .本文证明了每个无 4 圈的平面图是 (4 ,1) 可选的 .     

关于图的(k,d)染色问题

对（ｋ,ｄ）染色问题的起源和进展民政部作了简要的回顾,总结了其已有研究成果;并对ＶｉｎｃｅＡＤ（１９８８）文中提出的问题给出了部分答案。     

Neutron activation analysis and Mössbauer spectroscopy research on coloring mechanism of ancient Chinese Guan porcelain

The content of 30 kinds of coloring elements in Guan porcelain in the Southern Song Dynasty has been determined by neutron activation analysis (NAA). Iron is the major coloring element. Mossbauer spectroscopy has shown that the iron of the glaze exists in the form of structural iron (Fe²⁺, Fe³⁺). The quantitative relationship between the main wavelength of every color glaze and the relative content (Fe²⁺/Fe³⁺) of structural iron has been determined. Thus the coloring mechanism of Guan porcelain in the Southern Song Dynasty has been revealed entirely.     

New mixed broadcast scheduling approach using neural networks and graph coloring in wireless sensor network

Due to the mutual interference and sharing of wireless links in TDMA wireless sensor networks, conflicts will occur when data messages are transmitting between nodes. The broadcast scheduling problem (BSP) is aimed to schedule each node in different slot of fixed length frame at least once, and the objective of BSP is to seek for the optimal feasible solution, which has the shortest length of frame slots, as well as the maximum node transmission. A two-stage mixed algorithm based on a fuzzy Hopfield neural network is proposed to solve this BSP in wireless sensor network. In the first stage, a modified sequential vertex coloring algorithm is adopted to obtain a minimal TDMA frame length. In the second stage, the fuzzy Hopfield network is utilized to maximize the channel utilization ratio. Experimental results, obtained from the running on three benchmark graphs, show that the algorithm can achieve better performance with shorter frame length and higher channel utilizing ratio than other exiting BSP solutions.     

奇圈、偶圈与轮的多重联图的邻点可区别E-全染色

G(V,E)是一个简单图,k是一个正整数,f是一个V(G)∪E(G)到{1,2,…,k}的映射,如果(A)uv∈E(G),则f(u)≠f(v),f(u)≠f(uv),f(v)≠f(uv),C(u)≠C(v),其中,C(u)={f(u)}∪{f(uv)|uvEE(G)},称f是图G的邻点可区别E-全染色,称最小的数k为图G的邻点可区别E-全色数,给出了奇圈、偶圈与轮的多重联图的邻点可区别E-全色数.     

2-连通外部平面图的平方图的列表染色

图G的平方图,记作G2,是一个以原图的顶点集作为顶点集,若原图中两点的距离不大于2则连以边所成的图.图G的列表染色数,记作lχ(G),定义为最小的自然数k,使得满足:对任一顶点给定k种颜色的列表,且染色时每个顶点的颜色只能从自身的颜色列表中选择时,总存在G顶点的一个正常染色.设G是一个最大度为Δ(G)的2-连通外部平面图,则lχ(G2)≤Δ(G)+2.     

关于强边着色猜想的最优图问题

著名图论专家Erd(o)s和Ne(s)et(r)il对图的强边着色数上界提出了一个猜想:当△为偶数时,x's(G)≤5/4△2;当△为奇数时,x's(G)≤1/4(5△2-2△+1),他们给出了当△=4的时的最优图.此处构造了一族图,并以此证明了当△为偶数时,如果Erd(o)s和Ne(s)et(r)il提出的强边着色猜想成立,则猜想中的上界是最优的.     

D(d)-VDTC猜想的反例

利用反证法及组合分析法, 得到一些更一般的D(d)-VDTC猜想的反例, 进一步说明了图的D(d)-点可区别全色数与其平凡下界之差可以超过任意正整数.     

极化曲线法比较彩色不锈钢在硫酸介质中的耐蚀性

通过化学着色法对304HC,316,316L不锈钢进行了着金黄色及其热水固膜后处理,运用动态极化曲线扫描法测定了其点蚀击穿电位,结果表明,3种不锈钢着色后的点蚀击穿电位提高80-100mV,耐蚀性能明显提高;热水固膜处理后的彩色不锈钢。304HC不锈钢的点蚀击穿电位又提高了80mV,耐腐蚀进一步增强。     

若干联图的星全染色

图G的一个正常全染色如果满足G中任意路长为2的点和边着色均不相同,称为G的星全染色.图的全部k-星全染色中所用最少的颜色数称为图G的星全色数.文章研究了若干联图的星全色数.