Collapsible biclaw-free graphs

A graph is called biclaw-free if it has no biclaw as an induced subgraph. In this note, we prove that if G is a connected bipartite biclaw-free graph with δ(G)?5, then G is collapsible, and of course supereulerian. This bound is best possible.     

TeV能区物理

文章简要介绍研究TeV能区物理的意义、重要性和当前国际上的发展形势,以及清华大学粒子物理理论组为发展TeV能区物理研究所做的工作和取得的成果.     

Balanced and 1-balanced graph constructions

There are several density functions for graphs which have found use in various applications. In this paper, we examine two of them, the first being given by b(G)=|E(G)|/|V(G)|, and the other being given by g(G)=|E(G)|/(|V(G)|−ω(G)), where ω(G) denotes the number of components of G. Graphs for which b(H)≤b(G) for all subgraphs H of G are called balanced graphs, and graphs for which g(H)≤g(G) for all subgraphs H of G are called 1-balanced graphs (also sometimes called strongly balanced or uniformly dense in the literature). Although the functions b and g are very similar, they distinguish classes of graphs sufficiently differently that b(G) is useful in studying random graphs, g(G) has been useful in designing networks with reduced vulnerability to attack and in studying the World Wide Web, and a similar function is useful in the study of rigidity. First we give a new characterization of balanced graphs. Then we introduce a graph construction which generalizes the Cartesian product of graphs to produce what we call a generalized Cartesian product. We show that generalized Cartesian product derived from a tree and 1-balanced graphs are 1-balanced, and we use this to prove that the generalized Cartesian products derived from 1-balanced graphs are 1-balanced.     

Conditional colorings of graphs

For an integer r>0, a conditional(k,r)-coloring of a graph G is a proper k-coloring of the vertices of G such that every vertex of degree at least r in G will be adjacent to vertices with at least r different colors. The smallest integer k for which a graph G has a conditional (k,r)-coloring is the rth order conditional chromatic number χ_r(G). In this paper, the behavior and bounds of conditional chromatic number of a graph G are investigated.     

On Circular Flows Of Graphs

A sufficient condition for graphs with circular flow index less than 4 is found in this paper. In particular, we give a simple proof of a result obtained by Galluccio and Goddyn (Combinatorica, 2002), and obtain a larger family of such graphs. * Partially supported by the National Security Agency under Grants MDA904-01-1-0022.     

Energy transfer probability in organic electrophosphorescence device with dopant

Based on the energy transfer process from host to dopant in an organic electrophosphorescent (EP) device, the expression of energy transfer probability ($\eta )$ between the host (TPD) and guest (Ir(ppy)$_{3})$ EP systems was proposed. The results show that: ({1}) The rate of the triplet energy transfer ($K_{\rm HG}$ and $K_{\rm GH})$ increases exponentially with increasing donor-acceptor molecular distance ($R$), whereas decreases as the intermolecular distance ($R_{\rm HH})$ increases from 0.8 to 2.4 nm. Furthermore, $K_{\rm GH}$ changes more quickly than $K_{\rm HG.}$ ({2}) The energy transfer probability ($\eta )$ increases as $R$ reduces, and the $R_{\rm HH}$ changes can be safely neglected for $R<$0.9 nm. The situation changes for 0.9nm$ < R < 1.1$nm, $R_{\rm HH }$ ($<1$nm) plays an essential role when $\eta $ changes and increases with the latter. However, if $R > 1.1$nm, the transfer probability will be below zero. Here, the energy transfer principle may be less important, and the high electroluminescence (EL) quantum efficiency of phosphorescent system will be attributed to the direct electron-hole recombination in phosphorescent molecules. ({3}) The $\eta $ will increase when the Forster radius ($R_{0})$ increases or Gibb's energy decreases.     

Duality in graph families

The concepts of complete and free families are studied by Catlin. It has been noted by Catlin that these concepts are, in some sense, dual to each other. In this paper, we investigate the duality between edge-contractions and edge-deletions, and establish some results dual to several Catlin's theorems.     

An <Emphasis Type="Italic">s</Emphasis>-Hamiltonian Line Graph Problem

For an integer k > 0, a graph G is k-triangular if every edge of G lies in at least k distinct 3-cycles of G. In (J Graph Theory 11:399–407 (1987)), Broersma and Veldman proposed an open problem: for a given positive integer k, determine the value s for which the statement “Let G be a k-triangular graph. Then L(G), the line graph of G, is s-hamiltonian if and only L(G) is (s + 2)-connected” is valid. Broersma and Veldman proved in 1987 that the statement above holds for 0 ≤ s ≤ k and asked, specifically, if the statement holds when s = 2k. In this paper, we prove that the statement above holds for 0 ≤ s ≤ max{2k, 6k − 16}.     

A highly efficient synthesis of 22-deoxy-OSW-1 by utilizing the intact skeleton of diosgenin

22-Deoxy-OSW-1 (1), an analogue of OSW-1 with the potent anticancer activity, was synthesized by utilizing the intact skeleton of diosgenin in 11 steps in 13.7% overall yield. This synthesis demonstrated an effective and reasonable synthetic strategy for bioactive steroids with side chains.