On edge colorings of 1-toroidal graphs

A graph is 1-toroidal, if it can be embedded in the torus so that each edge is crossed by at most one other edge. In this paper, it is proved that every 1-toroidal graph with maximum degree Δ≥ 10 is of class one in terms of edge coloring. Meanwhile, we show that there exist class two 1-toroidal graphs with maximum degree Δ for each Δ≤ 8.     

A sufficient condition for planar graphs with maximum degree 8 to be 9-totally colorable

A total k-coloring of a graph G is a coloring of V(G) ∪ E(G) using k colors such that no two adjacent or incident elements receive the same color. The total chromatic number χ'(G) is the smallest integer k such that G has a total k-coloring. It is known that if a planar graph G has maximum degree Δ≥ 9, then χ'(G) = Δ + 1. In this paper, we prove that if G is a planar graph with maximum degree 8 and without a fan of four adjacent 3-cycles, then χ'(G) = 9.     

关于图的3-条件色数

For integers k0,r0,a(k,r)-coloring of a graph G is a proper k-coloring of the vertices such that every vertex of degree d is adjacent to vertices with at least min{d,r}diferent colors.The r-hued chromatic number,denoted byχr(G),is the smallest integer k for which a graph G has a(k,r)-coloring.Define a graph G is r-normal,ifχr(G)=χ(G).In this paper,we present two sufcient conditions for a graph to be 3-normal,and the best upper bound of 3-hued chromatic number of a certain families of graphs.     

联图的关联着色

图G的一个κ-关联着色是指从G的关联集I(G)到颜色集{1,2,…,κ}的一个映射,满足任意一对相邻的关联分配到不同的颜色.使得G有κ-关联着色的最小的数κ称为G的关联色数,记为X_i(G).研究了联图的关联着色,给出了G∨H的关联色数的一个上界,讨论了路与路,路与圈,圈与圈的联图的关联色数.     

Wet-spinning of Regenerated Silk Fiber fromAqueous Silk Fibroin Solutions: Influence ofCalcium Ion Addition in Spinning Dope on thePerformance of Regenerated Silk Fiber简

Ca（II） ions are added in the spinning dope to adjust the solidification rate of regenerated silk fibroin （RSF） solution during the wet-spinning process since Ca（II） ions are proved to be favorable to maintain the stable silk fibroin network in our previous work. The results show that when Ca（II）/RSF ratios are 1/50 and 1/20, the resulted RSF fibers exhibit good performance with the breaking energy more than 70 kJ/kg. However, higher Ca（II）/RSF ratio （for example, 1/10） hinders the solidification of spinning dope and results in poor RSF fibers. These observations together with earlier papers from this laboratory confirm that to produce tough silk fibers the spinning conditions must allow sufficient time for the adjustment of silk fibroin molecular chains.     

单圈图和双圈图的连续边着色

设G是简单图,用颜色1,2,3,…对G的边正常着色,如果在每一顶点表现的颜色构成一个连续的整数集合,那么就称这个着色是连续的.图G的亏度def(G)是粘在G上使得它可连续着色的悬挂边的最小数目.在本文中,我们完全确定了单圈图和双圈图的亏度.     

图的关联色数和关联着色猜想

本文综述了图的关联着色的已有结果，证明了关联着色猜想对于完全3—部图和高度留成立，确定了路、圈、扇、轮和加边轮等特殊图类的关联色数．     

图的围长与无圈边色数之间的关系

对于一个图G的正常边着色，如果此种边着色使得该图没有2—色的圈，那么这种边着色被称为是G的无圈边着色．用d(G)表示图G的无圈边色数，即G的无圈边着色中所使用的最小颜色数．Alon N，Sadakov B and Zaks A在[1]中有如下结果：对于围长至少是2000△(G)log△(G)的图G，有d(G)≤△ 2，其中△是图G的最大度．我们改进了这个结果，得到了如下结论：对于围长至少是700△(G)log△(G)的图G，有d(G)≤△ 2．     

边着色路到完全图的嵌入

一、一个猜想设 P_n 为具有 n 个顶点的一条路,它的 n-1条边着上了不同的颜色,若这个着色能扩充为 n 个顶点的完全图 K_n 的一个正常的 x′(K_n)一边着色,则称边着色路 P_n 能嵌入于完全图.一般说来,设 G 是具有边色数 x′(G)的一个简单图,令 M(G)为 G 中所有满足以下性质的子图 H(?)G 的集合:存在 G 的一种正常的 x′(G)-边着色使得 H 的各条边具有不同的颜色.设 K_n 是 n 个顶点的完全图,把集合 M(K_n)简记为 M_n 于是我们一开始提出的问题“P_n 能否嵌入于完全图”等价于“P_n 是否属于 M_n”.     

采用Ag+离子与TiF6光学玻璃内的K+或Na+离子交换产生高折射率梯度剖面分布

本文介绍了TiF₆光学玻璃的制作。研究了这种玻璃内的K⁺或Na⁺离子与Ag⁺离子交换。使用双光束干涉法观测了干涉纹、并用电子探针扫描电镜测量了Ag⁺、K⁺和Na⁺离子的浓度分布,还着重研究了离子交换后的玻璃裂纹和着色问题。最后,对结果作了讨论。