关于控制临界数(英)

本文给出控制临界数的一系列上界，且刻划了控制临界数为△＋1的图的特征．     

关于竞赛图的完备强路连通性的一个充要条件

在本文定理2中!证明了如下结果:p个顶点的竞赛图T=(V,A)是完备强路连通的充要条件是对T中任一弧,在T中总存在对应这弧的P_2、P′_2、P′_(p-1)、P′(p-1). 本文提出如下猜测:p个顶点的竞赛图T=(V,A)中的任一弧,在T中总存在对应这弧的 P′_2、P′_(p-1),则T具有强路连通性.     

恰含d个非零对角元的本原矩阵的广义最大密度指数集

设Ａ是一个具有周期ｐ的ｎ×ｎ不可约布尔矩阵,文［１］定义了矩阵的广义最大密度指数ｈＡ（ｋ）令ＤＩＳｎ,ｄ（ｋ）＝｛ｈＡ（ｋ）｜ Ａ ＰＭｎ（ｄ）｝,其中ＰＭｎ（ｄ）是所有恰含ｄ个非零对角元的ｎ×ｎ本原矩阵的集合．本文证明了另外,我们定义矩阵Ａ的范数,用Ａ表示,为Ａ中１的个数,并且刻划了具有最小范数的极矩阵．     

直径为d的超环面网的(d,2n)-控制数

n维超环面网C(dl,d2,…,dn)定义如下顶点集为{(x1,..,xn)|0≤xi<di(1≤i≤n)};每个顶点(xl,…,xn)与(x1±1,x2,…,xn),(xl,x2±1,…,xn),…,(x1,x2,….,xn±1)这2n个顶点相邻.(d,m)-控制数是用来刻画互连网络数据传输某种模式的一个新参数.本文证明了当d=diam(C(d1,d2,…,dn))时,n维超环面网C(d1,d2,…,dn)≠C(3,3,….,3)的(d,2n)控制数为2(n≥3,di≥3,i∈{1,2,…,n}.     

超图中的着色问题

本文是近三十年来有关超图中涉及的着色问题的综述。它包含了有关超图着色中的基本结果,临界可着色性,２－可着色性,非２－可着色性以及在超图中与顶点着色、边着色和其它着色相关的极值问题。     

THE BROADCAST FUNCTION VALUE B(23) IS 33 OR 34

1. IntroductionLet G be a connected network of order n. Broadcasting is the process of distributinginformation from an originator to all other nodes of a communication network. The problemaddressed in this paper is under the assumption that only one piece information is to bedistributed, each communication involves exactly two adjacent nodes and takes one unit oftime, and no node is involved into two or more simultaneous communications. Given a nodex as originator, we define the broadcast tim…     

关于κ-超竞赛图的度序列

本文对３－超竞赛图的度序列给出了一个充要条件,并且推广了竞赛图中相应的结果．     

Outpaths of arcs in multipartite tournaments

1. IntroductionThroughout the paPer, we use the terminology and notation of [1] and [2]. Let D =(V(D), A(D)) be a digraPh. If xy is an arc of a digraPh D, then we say that x dominatesy, denoted by x - y. More generally, if A and B are two disjoint vertex sets of D such thatevery vertex of A dominates every vertex of B, then we say that A dominates B, denotedby A - B. The outset N (x) of a vertex x is the set of vertices dominated by x in D,and the inset N--(x) is the set of vertices d…     

A SEVEN-COLOR THEOREM ON EDGE-FACE COLORING OF PLANE GRAPHS

1 IntroductionLet G be a plane graph with the vertex set V(G), the edge set E(G), the faCe set F(G),and the maximum degree A(G). The edge-face chromatic number X.I (G) of G is the ndnimumnunther of colors assigned to E(G) U F(G) such that aliy two adjacent or incident elements havedifferent colors. By the definition, X.,(G) 2 A(G) is trivial. In 1975, MelnikovI4J raised thefollowing conjecture.,Coniecture 1.1 For every plane graph G, X.J (G) 5 A(G) 3.The conjecture has been ton…     

关于非负矩阵的幂序列的注记

n阶非负方阵,当它是不可约时,它的幂收敛指数、最大密度指数的上界为O(n~2),特别当A是本原时,这两种指数相等,且有精确上界W_n=(n-1)~2+1。但对一般的非负矩阵,本文指出:当n→∞时,它的最大密度指数的上界的无穷大阶比任何幂函数均要高。