The size of graphs without nowhere-zero 4-flows

Let G be a 2-edge-connected simple graph with order n. We show that if | V(G)| ≤ 17, then either G has a nowhere-zero 4-flow, or G is contractible to the Petersen graph. We also show that for n large, if | V(G)| n ? 17/2 + 34, then either G has a nonwhere-zero 4-flow, or G can be contracted to the Petersen graph. © 1995 John Wiley & Sons, Inc.     

高温高压下SrB4O7：Eu2+玻璃的晶化

 利用X射线衍射和Eu²⁺发射光谱方法研究了非晶玻璃SrB₄O₇在高温高压下的晶化。结果表明：在5.0 GPa压力下，200 ℃仍为玻璃态，只有几个强度极低的小峰，表明有晶化的迹象；600 ℃时已基本晶化，但为SrB₄O₇正交相与SrB₄O₇高压立方相二相共存；当温度提高到1 000 ℃时，晶化成了近单相的与常压SrB₄O₇粉末晶体相同的正交结构。伴随晶化度的加强，Eu²⁺发射强度增强，与Ｘ射线衍射结果相一致。     

有机层界面对双层有机发光二极管复合效率的影响

建立了双层有机发光二极管中载流子在有机层界面复合的无序跳跃理论模型.由于有机分子材料的空间及能带结构的无序性，采用刚体模型处理有机层界面问题是不恰当的，而采用无序跳跃模型比较合理.复合效率及复合电流由载流子跳跃距离、有机层界面的有效势垒高度及该界面处的电场强度分布所决定：在双层器件ITO/α-NPD/Alq₃/Al中，当所加电压小于19.5V时，复合效率随着载流子跳跃距离的增加而增加，而大于19.5V时，复合效率随着其距离的增加而减少；复合效率随着有机层界面有效势垒高度的增加而增加； 关键词： 有机层界面 双层有机发光二极管 复合效率 有效势垒高度 无序跳跃模型     

载流子迁移率对单层有机发光二极管复合效率的影响

建立了在单层有机发光二极管中电场强度不太大(E≤104Vcm)的情况下,载流子注入、传输和复合的理论模型.通过求解非线性Painleve方程得出了电场强度随坐标变化的解析函数关系式以及电流密度随电压变化关系,给出了电流密度以及器件的复合效率在不同的载流子迁移率情况下随电压变化关系图像.结果表明,复合效率受载流子迁移率影响较大,在器件中多数载流子应具有较低的迁移率,而少数载流子应具有较高的迁移率,这样有利于载流子的注入和传输,从而可提高发光效率.并且得出当空穴迁移率大于电子迁移率时,复合区域偏向阴极,反之亦 关键词： 单层有机发光二极管 复合效率 迁移率     

Group connectivity in line graphs

Tutte introduced the theory of nowhere zero flows and showed that a plane graph G has a face k-coloring if and only if G has a nowhere zero A-flow, for any Abelian group A with |A|≥k. In 1992, Jaeger et al. [9] extended nowhere zero flows to group connectivity of graphs: given an orientation D of a graph G, if for any b:V(G)?A with ∑_v∈V(G)b(v)=0, there always exists a map f:E(G)?A−{0}, such that at each v∈V(G), in A, then G is A-connected. Let Z₃ denote the cyclic group of order 3. In [9], Jaeger et al. (1992) conjectured that every 5-edge-connected graph is Z₃-connected. In this paper, we proved the following.

• (i) 

  Every 5-edge-connected graph is Z3-connected if and only if every 5-edge-connected line graph is Z3-connected.

• (ii) 

  Every 6-edge-connected triangular line graph is Z3-connected.

• (iii) 

  Every 7-edge-connected triangular claw-free graph is Z3-connected.

In particular, every 6-edge-connected triangular line graph and every 7-edge-connected triangular claw-free graph have a nowhere zero 3-flow.     

An inequality for the group chromatic number of a graph

We give an inequality for the group chromatic number of a graph as an extension of Brooks’ Theorem. Moreover, we obtain a structural theorem for graphs satisfying the equality and discuss applications of the theorem.     

On Group Connectivity of Graphs

Tutte conjectured that every 4-edge-connected graph admits a nowhere-zero Z ₃-flow and Jaeger et al. [Group connectivity of graphs–a nonhomogeneous analogue of nowhere-zero flow properties, J. Combin. Theory Ser. B 56 (1992) 165-182] further conjectured that every 5-edge-connected graph is Z ₃-connected. These two conjectures are in general open and few results are known so far. A weaker version of Tutte’s conjecture states that every 4-edge-connected graph with each edge contained in a circuit of length at most 3 admits a nowhere-zero Z ₃-flow. Devos proposed a stronger version problem by asking if every such graph is Z ₃-connected. In this paper, we first answer this later question in negative and get an infinite family of such graphs which are not Z ₃-connected. Moreover, motivated by these graphs, we prove that every 6-edge-connected graph whose edge set is an edge disjoint union of circuits of length at most 3 is Z ₃-connected. It is a partial result to Jaeger’s Z ₃-connectivity conjecture. Received: May 23, 2006. Final version received: January 13, 2008     

Spanning Trails Connecting Given Edges

Suppose that is the set of connected graphs such that a graph G if and only if G satisfies both (F1) if X is an edge cut of G with |X|3, then there exists a vertex v of degree |X| such that X consists of all the edges incident with v in G, and (F2) for every v of degree 3, v lies in a k-cycle of G, where 2k3.In this paper, we show that if G and (G)3, then for every pair of edges e,fE(G), G has a trail with initial edge e and final edge f which contains all vertices of G. This result extends several former results.