Abstract:
Let $G$ be a connected simple graph of order $n$ and let $\Delta(G)$ and $\chi'(G)$ denote the maximum degree and chromatic index of $G$, respectively. Vizing proved that $\chi'(G)=\Delta(G)$ or $\Delta(G)+1$. Following this result, $G$ is called $\Delta$-critical if $\chi'(G)=\Delta(G)+1$ and $\chi'(G-e)=\Delta(G)$ for every $e\in E(G)$. In 1968, Vizing conjectured that if $G$ is an $n$-vertex $\Delta$-critical graph, then the independence number $\alpha(G)\le n/2$. Furthermore, he conjectured that, in fact, $G$ has a 2-factor. Luo and Zhao showed that if $G$ is an $n$-vertex $\Delta$-critical graph with $\Delta(G)\ge n/2$, then $\alpha(G)\le n/2$. More recently, they showed that if $G$ is an $n$-vertex $\Delta$-critical graph with $\Delta(G)\ge 6n/7$, then $G$ has a hamiltonian cycle, and so $G$ has a 2-factor. In this paper, we show that if $G$ is an $n$-vertex $\Delta$-critical graph with $\Delta(G)\ge n/2$, then $G$ has a 2-factor.

Abstract:
The square of a graph is obtained by adding additional edges joining all pair of vertices of distance two in the original graph. Particularly, if $C$ is a hamiltonian cycle of a graph $G$, then the square of $C$ is called a hamiltonian square of $G$. In this paper, we characterize all possible forbidden pairs, which implies the containment of a hamiltonian square, in a 4-connected graph. The connectivity condition is necessary as, except $K_3$ and $K_4$, the square of a cycle is always 4-connected.

Abstract:
Let $G$ be an $n$-vertex graph with $n\ge 3$. A classic result of Dirac from 1952 asserts that $G$ is hamiltonian if $\delta(G)\ge n/2$. Dirac's theorem is one of the most influential results in the study of hamiltonicity and by now there are many related known results\,(see, e.g., J. A. Bondy, Basic Graph Theory: Paths and Circuits, Chapter 1 in: {\it Handbook of Combinatorics Vol.1}). A {\it Halin graph}, which consists of a plane tree with no vertices of degree 2 and a cycle connecting its leaves according to the cyclic order determined by the embedding, possesses rich hamiltonicity properties such as being hamiltonian, hamiltonian connected, and almost pancyclic. As a continuous "generalization" of Dirac's theorem, in this paper, we show that there exists a positive integer $n_0$ such that any graph $G$ with $n\ge n_0$ vertices and $\delta(G)\ge (n+1)/2$ contains a spanning Halin subgraph.

Abstract:
A spanning tree with no vertices of degree 2 is called a Homeomorphically irreducible spanning tree\,(HIST). Based on a HIST embedded in the plane, a Halin graph is formed by connecting the leaves of the tree into a cycle following the cyclic order determined by the embedding. Both of the determination problems of whether a graph contains a HIST or whether a graph contains a spanning Halin graph are shown to be NP-complete. It was conjectured by Albertson, Berman, Hutchinson, and Thomassen in 1990 that a {\it every surface triangulation of at least four vertices contains a HIST}\,(confirmed). And it was conjectured by Lov\'asz and Plummer that {\it every 4-connected plane triangulation contains a spanning Halin graph}\,(disproved). Balancing the above two facts, in this paper, we consider generalized Halin graphs, a family of graph structures which are "stronger" than HISTs but "weaker" than Halin graphs in the sense of their construction constraints. To be exact, a generalized Halin graph is formed from a HIST by connecting its leaves into a cycle. Since a generalized Halin graph needs not to be planar, we investigate the minimum degree condition for a graph to contain it as a spanning subgraph. We show that there exists a positive integer $n_0$ such that any 3-connected graph with $n\ge n_0$ vertices and minimum degree at least $(2n+3)/5$ contains a spanning generalized Halin graph. As an application, the result implies that under the same condition, the graph $G$ contains a wheel-minor of order at least $n/2$. The minimum degree condition in the result is best possible.

Abstract:
Let S_m denote the m-vertex simple digraph formed by m-1 edges with a common tail. Let f(m) denote the minimum n such that every n-vertex tournament has a spanning subgraph consisting of n/m disjoint copies of S_m. We prove that m lg m - m lg lg m <= f(m) <= 4m^2 - 6m for sufficiently large m.

Abstract:
When we study forbidden subgraph conditions guaranteeing graphs to have some properties, a claw (or $K_{1,3}$) frequently appears as one of forbidden subgraphs. Recently, Furuya and Tsuchiya compared two classes generated by different forbidden pairs containing a claw, and characterized one of such classes. In this paper, we give such characterization for three new classes. Furthermore, we give applications of our characterizations to some forbidden subgraph problems.

Abstract:
We report applications of language technology to analyzing historical documents in the Database for the Study of Modern Chinese Thoughts and Literature (DSMCTL). We studied two historical issues with the reported techniques: the conceptualization of "huaren" (Chinese people) and the attempt to institute constitutional monarchy in the late Qing dynasty. We also discuss research challenges for supporting sophisticated issues using our experience with DSMCTL, the Database of Government Officials of the Republic of China, and the Dream of the Red Chamber. Advanced techniques and tools for lexical, syntactic, semantic, and pragmatic processing of language information, along with more thorough data collection, are needed to strengthen the collaboration between historians and computer scientists.

Abstract:
Colorectal cancer (CRC) is one of the most commonly diagnosed cancers in the world. A genome-wide screening of transcriptome dysregulation between cancer and normal tissue would provide insight into the molecular basis of CRC initiation and progression. Compared with microarray technology, which is commonly used to identify transcriptional changes, the recently developed RNA-seq technique has the ability to detect other abnormal regulations in the cancer transcriptome, such as alternative splicing, novel transcripts or gene fusion. In this study, we performed high-throughput transcriptome sequencing at ~50× coverage on CRC, adjacent non-tumor and distant normal tissue. The results revealed cancer-specific, differentially expressed genes and differential alternative splicing, suggesting that the extracellular matrix and metabolic pathways are activated and the genes related to cell homeostasis are suppressed in CRC. In addition, one tumor-restricted gene fusion, PRTEN-NOTCH2, was also detected and experimentally confirmed. This study reveals some common features in tumor invasion and provides a comprehensive survey of the CRC transcriptome, which provides better insight into the complexity of regulatory changes during tumorigenesis.

Abstract:
The study of yaw variations of a in-bore projectile and related factors is one of the important aspects of launch dynamics Measurements of yaw variations of a in-bore projectile is a prerequisite to accomplish the study. Thus, lots of papers on this aspect have been published.This paper introduced a measuring system using high-speed camea and laser source. The characteristic of the system are as follows:1) The variation with time of yaw rotation speed of the in-bore projectile and the vibration of the gun tube can be measured simultaneously.2) Photographs can be taken at day time.3) Because any parablic mirror is not used in the optical system, the cost is reduced greatly.4) we can adjust and dispose the optical system of the camera to utilize fully the nagative to record the message.The results of firing test showed that the system was feasible, By use of the system we have obtained the yaw curves of the in-bpre projectile.

Abstract:
The traditional classical incentive model only reveals the general rule of organizational incentive, and does not give specific operation rules. The matching between organizational incentives and employee needs is still black box, and it does not reveal its core operation mechanism from the perspective of mechanism. This paper took through the literature review, the Hidilao Hotpot company as a case study, through a variety of ways to collect data, the use of grounded theory to encode data analysis, and ultimately extracted 58 concepts, 26 sub-areas, 7 main areas, concluded that the Hidilao Hotpot Employee motivation formed the path, and ultimately extracted the micro-level employee motivation mechanism model. The research result of this article comes from the practice of the enterprise, which has enlightenment to the organizational incentive of the traditional catering industry and also provides a micro-research perspective and systematic mechanism research for the incentive field.