Numerical conformal mapping of multiply connected regions onto the second, third and fourth categories of Koebe?s canonical slit domains

This paper presents a boundary integral method for approximating the conformal mappings from any bounded or unbounded multiply connected region G onto the second, third and fourth categories of Koebe?s canonical slit domains. The method can be also used for calculating the conformal mappings of simply and doubly connected regions. The method is an extension of the author?s method for the first category of Koebe?s canonical slit domains (see [M.M.S. Nasser, Numerical conformal mapping via a boundary integral equation with the generalized Neumann kernel, SIAM J. Sci. Comput. 31 (2009) 1695-1715]). Three numerical examples are presented to illustrate the performance of the proposed method.     

Line graphs of multigraphs and Hamilton‐connectedness of claw‐free graphs

We introduce a closure concept that turns a claw‐free graph into the line graph of a multigraph while preserving its (non‐)Hamilton‐connectedness. As an application, we show that every 7‐connected claw‐free graph is Hamilton‐connected, and we show that the well‐known conjecture by Matthews and Sumner (every 4‐connected claw‐free graph is hamiltonian) is equivalent with the statement that every 4‐connected claw‐free graph is Hamilton‐connected. Finally, we show a natural way to avoid the non‐uniqueness of a preimage of a line graph of a multigraph, and we prove that the closure operation is, in a sense, best possible. © 2010 Wiley Periodicals, Inc. J Graph Theory 66:152‐173, 2011     

图模式挖掘中的子图同构算法

图模式挖掘问题在Web挖掘、生物信息学、社会关系等众多领域有广泛的应用,它涉及到子图的搜索以及子图的同构问题.这两个问题都具有相当高的计算复杂度,现有的子图同构问题大多采用最小编码算法,但对无标签图特别是对无标签无向图,该算法效率较底,从而子图的同构成为图模式挖掘问题的一个瓶颈.针对无标签图,以代数理论为基础,分别利用度序列和特征值构造了两种子图同构算法,用于对有向图和无向图的同构判别.最后对2个真实生物网络进行了仿真实验,结果表明,算法的效率优于现有算法.     

Analytic combinatorics of connected graphs

We enumerate the connected graphs that contain a number of edges growing linearly with respect to the number of vertices. So far, only the first term of the asymptotics and a bound on the error were known. Using analytic combinatorics, that is, generating function manipulations, we derive a formula for the coefficients of the complete asymptotic expansion. The same result is derived for connected multigraphs.     

带约束条件集值优化问题近似Henig有效解集的连通性

研究了带约束条件集值优化问题近似Henig有效解集的连通性.在实局部凸Hausdorff空间中,讨论了可行域为弧连通紧的,目标函数为C-弧连通的条件下,带约束条件集值优化问题近似Henig有效解集的存在性和连通性.并给出了带约束条件集值优化问题近似Henig有效解集的连通性定理.     

极小拟(k+1)连通图的最小度

给出了极小拟5连通图有围长大于或等于4的极小拟（k）＋1连通图的最小度。     

Vertex pancyclicity in quasi claw-free graphs

This paper generalizes the concept of locally connected graphs. A graph G is triangularly connected if for every pair of edges e₁,e₂∈E(G), G has a sequence of 3-cycles C₁,C₂,…,C_l such that e₁∈C₁,e₂∈C_l and E(C_i)∩E(C_i+1)≠∅ for 1?i?l-1. In this paper, we show that every triangularly connected quasi claw-free graph on at least three vertices is vertex pancyclic. Therefore, the conjecture proposed by Ainouche is solved.     

Cubic planar hamiltonian graphs of various types

Let U be the set of cubic planar hamiltonian graphs, A the set of graphs G in U such that G-v is hamiltonian for any vertex v of G, B the set of graphs G in U such that G-e is hamiltonian for any edge e of G, and C the set of graphs G in U such that there is a hamiltonian path between any two different vertices of G. With the inclusion and/or exclusion of the sets A,B, and C, U is divided into eight subsets. In this paper, we prove that there is an infinite number of graphs in each of the eight subsets.