k元de Bruijn-Good图的1-因子图与分配多面体图

本文首先修正了文献[2]中的定义1.2,然后给出了由κ元(?)级 de Bruijn-Good图的1-因子构成的变换图的结构,得到了它与分配多面体图(graph of assign-ment polytope)的关系,从而得知它具有一些好的性质.     

The impact of 2-neighborhoods on graph structure

Connected regular graphs of diameter greater than 2 with 2-neighborhoods isomorphic to a certain graph Δ of diameter 2 are studied. Regular graphs of diameter 2 with 2-neighborhoods isomorphic to the distance-regular graph Δ of diameter 3 are also studied. It is prowed that 2-locally Schrikhande graphs do not exist. Translated fromMatematicheskie Zametki, Vol. 62, No. 6, pp. 892–897, December, 1997. Translated by S. S. Anisov     

数坛怪杰爱尔特希

匈牙利数学家爱尔特希(Erdos,P.)是世界沃尔夫数学大奖得主之一.本文仅从几个侧面,介绍其数学生涯,评述其数学思想、工作特色.     

图半群

构造了图半群,并证明两个拟简单图同构的充要条件是其相应的图半群同构;讨论了图半群、子图半群的一些性质;引进有向图半群,并讨论了它与严格有向图的关系.     

Hamiltonian[k,k+1]-因子

本文考虑n/2-临界图中Hamiltonian[k,k+1]-因子的存在性。Hamiltonian[k,k+1]-因子是指包含Hamiltonian圈的[k,k+1]-因子;给定阶数为n的简单图G,若δ(G)≥n/2而δ(G\e)相似文献   

ENTIRE CHROMATIC NUMBER AND △-MATCHING OF OUTERPLANE GRAPHS

Let G be an outerplane graph with maximum degree △ and the entire chromatic number χvef (G). This paper proves that if △≥ 6, then △ 1 ≤χvef (G) ≤△ 2,and χvef (G) = △ 1 if and only if G has a matching M consisting of some inner edges which covers all its vertices of maximum degree.     

The traveling salesman problem in graphs with some excluded minors

Given a graph and a length function defined on its edge-set, the Traveling Salesman Problem can be described as the problem of finding a family of edges (an edge may be chosen several times) which forms a spanning Eulerian subgraph of minimum length. In this paper we characterize those graphs for which the convex hull of all solutions is given by the nonnegativity constraints and the classical cut constraints. This characterization is given in terms of excluded minors. A constructive characterization is also given which uses a small number of basic graphs.