Longest Cycles in 3-Connected, K_(1,3)-Free Graphs

The graph considered in this paper is an undireeted graph of order n,without loops alld multiple edges.Denotea by V(G)the vertex set of graph G,by |V(G)| the cardinality of V(G),by K(G)the connectivity of G,by δ the minimum degree of G.A eyele in G is considered as a Subgraph of G,and for a Subgraph H of G.1et G-H denote the Subgraph of G inducedby vertex set V(G)-y(日).M. M.Marthews and D.P.Summer proved in 1986 that eVery 2-eonneeted, K_1,3-free     

图中有边不交的3个1─因子的一个新充分条件

Ｗｉｎ于１９８２年证明了２ｎ阶Ｏｒｅ－（１）型图有边不交的３个１－因子．本文改进这个结果，得到一个新的充分条件：２ｎ（ｎ≥１０）阶２－连通Ｏｒｅ－（－２）型图Ｇ有边不交的１个Ｈａｍｉｌｔｏｎ图和１个１－因子，除非Ｇ是附图中所示的图之一．     

图中有边不义的3个1—因子的一个新充分条件

ｉｎ于１９８２年证明了２ｎ阶Ｏｒｅ－（１）型图有边不交的３个１－因子。本文改进这个结果，得到一个新的充分条件：２ｎ（ｎ≥１０）阶２－连通Ｏｒｅ－（－２）型图Ｇ有边不变的１个Ｈａｍｉｌｔｏｎ图和１个１－因子，除非Ｇ是附图中所示的图之一。     

有偏单位元的环

在[2]、[3]文中建立了与[1]文中相平行的ρ—理想理论,本文将证明有偏单位元的ρ—交换环、ρ—理想、ρ—素理想、广义ρ—素理想、ρ—准素理想、ρ—互质、ρ—相关等概念与通常的概念完全一致,因此,关于满足ρ—理想极大条件、有偏单位元、ρ—交换环的ρ—理想分解定理实际上是Noether环的分解定理。本文还将给出一个理想与ρ—理想一致的充分条件。     

Longest Cycles in 2-Connected Regular Claw-Free Graphs

All graph considered In this paper are undirected and finite,without loops ormultip1e edges.A graph is called claw-free if it does not contain a copy of K_(1,3)as an induced subgraph.For a graph C,let δ(G)denote the minimum degree of G.There have been a great many results in recent years dealing with longest cycles.for example, M.Matthews and D.Summer have shown the following result:     

无$K_{1,4}$子图的图的路覆盖

For a graph G, a path cover is a set of vertex disjoint paths covering all the vertices of G, and a path cover number of G, denoted by p(G), is the minimum number of paths in a path cover among all the path covers of G. In this paper, we prove that if G is a K_(1,4)-free graph of order n and σ_(k+1)(G) ≥ n-k, then p(G) ≤ k, where σ_(k+1)(G) = min{∑v∈S d(v) : S is an independent set of G with |S| = k + 1}.     

一种噪声启发式聚类算法

启发式聚类算法的搜索空间中布满了局部极小值"陷阱",从而使得算法容易过早收敛而无法获得高质量聚类结果.文章给出了一种噪声启发式聚类算法NHCA (Noising Heuristic Clustering Algorithm),该算法在搜索空间中增加一组由强至弱的噪声来扩大启发式搜索的局部范围,以保持搜索空间的多样性,达到避免局部极小值影响和提高聚类质量的目的.大量实验结果表明,噪声法对提高启发式聚类算法质量是十分有效的.     

无爪图中的最长圈

本文证明了:n阶3—连通无爪图G中的最长圈的长至少为min{4k—5,n},这里k是G的最小度.     

半无爪可迹图的度和条件

可迹图即为一个含有Hamilton路的图.令$N[v]=N(v)\cup\{v\}$, $J(u,v)=\{w\in N(u)\cap N(v):N(w)\subseteq N[u]\cup N[v]\}$.若图中任意距离为2的两点$u,v$满足$J(u,v)\neq \emptyset$,则称该图为半无爪图.令$\sigma_{k}(G)=\min\{\sum_{v\in S}d(v):S$为$G$中含有$k$个点的独立集\},其中$d(v)$表示图$G$中顶点$v$的度.本论文证明了若图$G$为一个阶数为$n$的连通半无爪图,且$\sigma_{3}(G)\geq {n-2}$,则图$G$为可迹图; 文中给出一个图例,说明上述结果中的界是下确界; 此外,我们证明了若图$G$为一个阶数为$n$的连通半无爪图,且$\sigma_{2}(G)\geq \frac{2({n-2})}{3}$,则该图为可迹图.