严格(d)-连通无圈超图的计数

研究了一般的标号严格(d)-连通无圈超图的计数,得到了n阶标号严格(d)-连通无圈超图的计数公式.     

无圈超图的计数

研究了标号超图的计数, 得到2个公式: 一个是关于严格(D)-连通无圈齐超图的显式计数公式, 另一个是关于线性无圈超图数目的递推公式.     

匀称无圈超图的计数

研究了标号匀称无圈超图的计数, 得到了一般的$n$阶标号r-匀称(d)-森林和n阶标号r-匀称(d)-真森林的递推公式,并分别得到了包含和不包含独立点的$n$阶标号森林的计数显式.     

无圈超图规模的进一步研究

本文在王建方给出的严格(d)-连通κ-匀齐无圈超图的规模的基础上,进一步研究n阶(d)-连通κ-匀齐无圈超图的规模和非严格(d)-连通κ-匀齐无圈超图的规模,并分别得到它们规模的上下界.     

严格非匀称线性超树的计数公式

本文应用容斥原理，得到了有n个顶点、m条边的严格非匀称标号线性无圈超图的计数公式。     

关于匀称超树数的猜想

1982年,毛经中对(k 1) p阶和q边的匀称超树的个数T_(k 1)(p,q)提出如下猜想:其余 易见,当k(?)1时,T(p, q) (q-1)~(?) p~p(?),故(*)成立将是标号树计数的Cayley公式在超图理论中的推广。 本书证明了上述猜想并得到一般超图的计数式。 定义 如果超图H (X,ε)是连通的且不含圈,则称H为一超树,若(?)E_i∈ε,|E_i|=M,则称H是匀称M秩超树。     

超图的路和圈

超图是离散数学中最一般最复杂的结构 .无圈超图已被证明在数据库设计中非常有用 .从关系数据的结构出发 ,建立了关于超图的路、连通性和圈的新的公理系统 .该系统与特殊情形———图是符合的 .引入了虚圈和实圈的概念 ,这是一对相关联的概念 .虚圈在特殊情形———图中不存在 ,退化掉了 .定义了超图圈的相关性和独立性 ,给出了超图中最大独立实圈数目的计数公式 ,对特殊情形———图 ,这个公式就是Euler公式 .     

图带宽和与其对偶超图带宽和的关系

设H=（E1,E2,…,Em）是集合X上的一个超图,一个1-1映射f:X→{1,2,…,|X|}称为H的一个标号,对H的任一标号f,BS（H,f）=∑(E∈H)max{|f(u)-f(v)|;u,v∈E}称为超图H的关于标号f的带宽和BS(H)=min{BS(H,f)|f是超图H的标号|}称为H的带宽和．论文研究图带宽和与其对偶超图的带宽和这两个参数间的关系．     

关于有向图与超图的计数

1980年,M.Hegde和M.R.Sridharan沿用R.C.Read的计数方法,得到了标号偶有向图和偶超图的计数公式。我们推广了[1]的结果,得到了恰有2k个奇度点的p阶有向图和(p,q)有向图,恰有k个奇度点的p阶超图和(p,q)超图的计数式。本文所讨论的图均指标号图。     

关于三圈连通标号图的计数公式

关于三圈连通标号图的计数公式张树生江西宁都固厚中学本文所指的图者是无向简单图。如果一个图恰好包含有ｍ个初级圈，那么就说这个图恰好包含有ｍ个单个的圈。Ｈａｒａｒｙ在［１］中提出了给定圈的个数的连通标号圈的计数问题。Ｒｅｎｙｉ在［２］中解决了单圈边通标号...     

Counting acyclic hypergraphs

Acyclic hypergraphs are analogues of forests in graphs. They are very useful in the design of databases. The number of distinct acyclic uniform hypergraphs withn labeled vertices is studied. With the aid of the principle of inclusion-exclusion, two formulas are presented. One is the explicitformula for strict (d)-connected acyclic hypergraphs, the other is the recurrence formula for linear acyclic hypergraphs.     

Counting acyclic hypergraphs

Acyclic hypergraphs are analogues of forests in graphs. They are very useful in the design of databases. The number of distinct acyclic uniform hypergraphs withn labeled vertices is studied. With the aid of the principle of inclusion-exclusion, two formulas are presented. One is the explicitformula for strict (d)-connected acyclic hypergraphs, the other is the recurrence formula for linear acyclic hypergraphs.     

On the discovery of the cycle-axiom of hypergraphs

In this paper, the path through which the cycle axiom of hypergraphs was discovered will be retraced. The long process of discovery will be described, in particular how acyclic hypergraphs originated from the study of relational database schemes and how cycles of hypergraphs originated from the study of acyclic hypergraphs.     

On Axioms Contituting the Foundation of Hypergraph Theory

Hypergraphs are systems of finite sets, being the most general structures in discrete mathematics and powerful tools in dealing with discrete systems. In general, a branch of mathematics is built on some axioms. Informational scientists introduced the acyclic axiom for hypergraphs. In this paper, we first list several results concerning acyclic hypergraphs, in order to show that Acyclic-Axioms constitute the foundation of acyclic hypergraph theory. Then we give the basic theorem which shows that the Cycle-Axiom covers the Acyclic-Axioms and constitutes the foundation of hypergraph theory.     

Enumeration of Maximum Acyclic Hypergraphs

Abstract Acyclic hypergraphs are analogues of forests in graphs.They are very useful in the design ofdatabases. In this article,the maximum size of an acvclic hypergraph is determined and the number of maximumγ-uniform acyclic hypergraphs of order n is shown to be (_(r-1)~n)(n(r-1)-r~2 2r)~(n-r-1).     

秩为r的本原超图的指数集(英文)

本文研究了超图的本原性质.运用图论方法,得到了具有秩r(≥3)的所有n阶本原有向超图的指数集,并刻划了其极超图.     

On the Existence of Friendship Hypergraphs

A 3‐uniform friendship hypergraph is a 3‐uniform hypergraph in which, for all triples of vertices x, y, z there exists a unique vertex w, such that , and are edges in the hypergraph. Sós showed that such 3‐uniform friendship hypergraphs on n vertices exist with a so‐called universal friend if and only if a Steiner triple system, exists. Hartke and Vandenbussche used integer programming to search for 3‐uniform friendship hypergraphs without a universal friend and found one on 8, three nonisomorphic on 16 and one on 32 vertices. So far, these five hypergraphs are the only known 3‐uniform friendship hypergraphs. In this paper we construct an infinite family of 3‐uniform friendship hypergraphs on 2^k vertices and edges. We also construct 3‐uniform friendship hypergraphs on 20 and 28 vertices using a computer. Furthermore, we define r‐uniform friendship hypergraphs and state that the existence of those with a universal friend is dependent on the existence of a Steiner system, . As a result hereof, we know infinitely many 4‐uniform friendship hypergraphs with a universal friend. Finally we show how to construct a 4‐uniform friendship hypergraph on 9 vertices and with no universal friend.