Regularity of vertex operator superalgebras

We prove that the regularity of a vertex operator superalgebra can be reduced to the semisimplicity of the category of its weak modules.Moreover,the rationality can be replaced by requiring that each 1/2Z+-graded module is a direct sum of irreducible weak modules.     

给定悬挂点数的双圈图中具有最小Hosoya指数的图

Let G be a graph. The Hosoya index Z（G） of a graph G is defined to be the total number of its matchings. In this paper, we characterize the graph with the smallest Hosoya index of bicyclic graphs with given pendent vertices. Finally, we present a new proof about the smallest Hosoya index of bicyclic graphs.     

若干冠图的邻点可区别V-全染色

应用构造染色函数法研究了冠图C_m·C_n、C_m·C_n的邻点可区别V-全染色.通过对P_m·C_n的邻点可区别V-全染色的研究巧妙给出了C_m·C_n邻点可区别V-全染色,并得到了这些图的邻点可区别V-全色数,从而验证了图的邻点可区别V-全染色猜想.     

小度数图的邻点可区别全染色

本文研究了最大度为3 且没有相邻最大度的图的邻点可区别全染色. 利用边剖分的方法, 构造了此类图更为一般的情形, 得到了它们的邻点可区别全色数的上界. 目前, 未找到最大度为3 的图且它的邻点可区别全色数是6. 本文的结果部分地回答了这个问题.     

Acyclic edge coloring of triangle-free 1-planar graphs

A proper edge coloring of a graph G is acyclic if there is no 2-colored cycle in G. The acyclic chromatic index of G, denoted by χ a(G), is the least number of colors such that G has an acyclic edge coloring. A graph is 1-planar if it can be drawn on the plane so that each edge is crossed by at most one other edge. In this paper, it is proved that χ a(G) ≤Δ(G) + 22, if G is a triangle-free 1-planar graph.     

小度数图的邻点可区别全染色

本文研究了最大度为3且没有相邻最大度的图的邻点可区别全染色.利用边剖分的方法,构造了此类图更为一般的情形,得到了它们的邻点可区别全色数的上界.目前,未找到最大度为3的图且它的邻点可区别全色数是6.本文的结果部分地回答了这个问题.     

Multigrid convergence acceleration for implicit and explicit solution of Euler equations on unstructured grids

The multigrid method is one of the most efficient techniques for convergence acceleration of iterative methods. In this method, a grid coarsening algorithm is required. Here, an agglomeration scheme is introduced, which is applicable in both cell‐center and cell‐vertex 2 and 3D discretizations. A new implicit formulation is presented, which results in better computation efficiency, when added to the multigrid scheme. A few simple procedures are also proposed and applied to provide even higher convergence acceleration. The Euler equations are solved on an unstructured grid around standard transonic configurations to validate the algorithm and to assess its superiority to conventional explicit agglomeration schemes. The scheme is applied to 2 and 3D test cases using both cell‐center and cell‐vertex discretizations. Copyright © 2009 John Wiley & Sons, Ltd.     

An exact DSatur-based algorithm for the Equitable Coloring Problem

This paper describes an exact algorithm for the Equitable Coloring Problem, based on the well known DSatur algorithm for the classic Coloring Problem with new pruning rules specifically derived from the equity constraint. Computational experiences show that our algorithm is competitive with those known in literature.     

On trees with a maximum proper partial 0-1 coloring containing a maximum matching

I prove that in a tree in which the distance between any two endpoints is even, there is a maximum proper partial 0-1 coloring such that the edges colored by 0 form a maximum matching.