A Class of Three‐Colorable Triangle‐Free Graphs

The chromatic number of a triangle‐free graph can be arbitrarily large. In this article, we show that if all subdivisions of K_{2, 3} are also excluded as induced subgraphs, then the chromatic number becomes bounded by 3. We give a structural characterization of this class of graphs, from which we derive an coloring algorithm, where n denotes the number of vertices and m the number of edges of the input graph.     

Forbidden induced subgraph characterizations of subclasses and variations of perfect graphs: A survey

A graph is perfect if the chromatic number is equal to the clique number for every induced subgraph of the graph. Perfect graphs were defined by Berge in the sixties. In this survey we present known results about partial characterizations by forbidden induced subgraphs of different graph classes related to perfect graphs. We analyze a variation of perfect graphs, clique-perfect graphs, and two subclasses of perfect graphs, coordinated graphs and balanced graphs.     

On the maximal domain of attraction of Tracy–Widom distribution for Gaussian unitary ensembles

The asymptotic distribution of the largest eigenvalue of various classes of random matrices has been shown to have the Tracy–Widom distribution. In this article, we prove that the standardised maximum of an independent and identically distributed sequence of random variables having the Tracy–Widom distribution arising from the Gaussian unitary ensemble belongs to the Gumbel domain of attraction.     

求解最大团问题的D函数正则化方法

最大团问题是一个经典的组合优化问题.在Motzkin和Straus的二次规划模型基础上,给出一种求解该问题的D函数正则化算法.通过引进D函数可以改善问题的凸性.几个标准考题的计算结果表明,该算法稳定有效.     

Gap,cosum and product properties of the θ′ bound on the clique number

In a paper published in 1978, McEliece, Rodemich and Rumsey improved the Lovász bound θ for the maximum clique problem. This strengthening has become well known under the name Lovász–Schrijver bound and is usually denoted by θ′. This article now deals with situations where this bound is not exact. To provide instances for which the gap between this bound and the actual clique number can be arbitrarily large, we establish homomorphy results for this bound under cosums and products of graphs. In particular we show that for circulant graphs of prime order there must be a positive gap between the clique number and the bound.     

Research on Community Structure in Bus Transport Networks

We abstract the bus transport networks （BTNs） to two kinds of complex networks with space L and space P methods respectively. Using improved community detecting algorithm （PKM agglomerative algorithm）, we analyze the community property of two kinds of BTNs graphs. The results show that the BTNs graph described with space L method have obvious community property, but the other kind of BTNs graph described with space P method have not. The reason is that the BTNs graph described with space P method have the intense overlapping community property and general community division algorithms can not identify this kind of community structure. To overcome this problem, we propose a novel community structure called N-depth community and present a corresponding community detecting algorithm, which can detect overlapping community. Applying the novel community structure and detecting algorithm to a BTN evolution model described with space P, whose network property agrees well with real BTNs＇, we get obvious community property.     

Research on Community Structure in Bus Transport Networks

We abstract the bus transport networks (BTNs) to two kinds of complex networks with space L and space P methods respectively. Using improved community detecting algorithm (PKM agglomerative algorithm), we analyze the community property of two kinds of BTNs graphs. The results show that the BTNs graph described with space L method have obvious community property, but the other kind of BTNs graph described with space P method have not. The reason is that the BTNs graph described with space P method have the intense overlapping community property and general community division algorithms can not identify this kind of community structure. To overcome this problem, we propose a novel community structure called N-depth community and present a corresponding community detecting algorithm, which can detect overlapping community. Applying the novel community structure and detecting algorithm to a BTN evolution model described with space P, whose network property agrees well with real BTNs', we get obvious community property.     

An error detection and recovery algorithm for the transmission of digital holography over noisy channels

Digitalization enables and expertise storage and transmission of holographic data. However, the reconstructed object image is vulnerable to transmission errors over the noisy channel. We present a novel algorithm of what we believe is the first approach to reduction of noise effects on digital holograms corrupted by transmission errors. To accomplish this work, we exploit new interdependencies on the interference holograms and develop a detection-based algorithm to detect error points and to identify the corresponding interference holograms with the largest errors. In the reconstruction process, the conventional four-step algorithm is used for the recovery of error-free points. In contrast, a three-step algorithm is employed to reconstruct error points by removing the largest error holograms. With accurate detection, the proposed algorithm is capable of recovering the object image from digital holograms with severe transmission errors. It is shown that the proposed algorithm provides much better reconstruction performances than the conventional four-step reconstruction algorithm in an error-prone environment.     

Clique‐inverse graphs of K3‐free and K4‐free graphs

The clique graph K(G) of a given graph G is the intersection graph of the collection of maximal cliques of G. Given a family ℱ of graphs, the clique‐inverse graphs of ℱ are the graphs whose clique graphs belong to ℱ. In this work, we describe characterizations for clique‐inverse graphs of K₃‐free and K₄‐free graphs. The characterizations are formulated in terms of forbidden induced subgraphs. © 2000 John Wiley & Sons, Inc. J Graph Theory 35: 257–272, 2000     

On the Clique-Transversal Number in （Claw,K4）-Free 4-Regular Graphs

A clique-transversal set D of a graph G is a set of vertices of G such that D meets all cliques of G.The clique-transversal number,denoted by τC(G),is the minimum cardinality of a clique-transversal set in G.In this paper,we first present a lower bound on τC(G) and characterize the extremal graphs achieving the lower bound for a connected(claw,K4)-free 4-regular graph G.Furthermore,we show that for any 2-connected(claw,K4)-free 4-regular graph G of order n,its clique-transversal number equals to [n/3].