关于带宽极值问题的两个结果

本文研究的问题是确定ｅ＊（ｐ,Ｂ）的值,也就是确定顶点数为ｐ、带宽为Ｂ的连通图Ｇ的最小边数,本文给出当Ｂ＝ｐ＋３／２和Ｂ＝ｐ／２＋２时的精确结果。     

关于等高k-毛虫树的带宽

图的带宽问题是图论的一个重要课题。然而 ,即使对毛长不等的单毛虫树 ,其带宽问题也是NP_完全的。利用Chv偄ｔａｌ的直径型带宽下界为工具 ,我们可以确定等高k_毛虫树的带宽     

图带宽的若干刻划

本文研究图的带宽的若干等价刻划以及相关的理论结果。     

球面经纬线网络的带宽

我们知道,确定一般图的带宽是NP-完全问题。.因而确定特殊图的带宽是一个很有实际意义而引人注目的问题。迄今为止,这方面的主要结果见文献[3,4,5]。1976年,A.K.Dewdney提出了(m,n)构形,即(m,n)-多重路,亦即球面上n条经线所构成的图的带宽。1982年麦结华和林诒勋独立地解决了此问题。本文的工作是在上述研究工作基础上所作的进一步推广和发展,即解决了麦结华提出的一个更为复杂的图类—球面上n条经线m条纬线所构成的图,即球面经纬线网络C_(m,n)的带宽问题。     

图的强乘积的带宽

本文讨论了由两个图的强乘积所导出的一些特殊图的带宽.     

关于完全多部图的带宽和的一个注记

本文得到完全多部图的带宽和的一个递推方程；并由此给出带宽和的一些精确值．     

图加一条边后的带宽和

令$BS(G,f)=\sum\limits_{uv\in E(G)}|f(u)-f(v)|$, 其中$f$为$V(G)\rightarrow\{1,2,\cdots,|V(G)|\}$的双射, 并称$BS(G)=\min\limits_{f}BS(G,f)$为图$G$的带宽和. 讨论顶点数为$n$的简单图$G$加上一条边$e\in\overline{E(G)}$后, 带宽和$BS(G+e)$与$BS(G)$的关系, 得其关系式$BS(G)+1\leq BS(G+e)\leq BS(G)+n-1$. 并证明此不等式中等号可取到, 即存在图$G_{1}$和$G_{2}$使得$BS(G_{1}+e)=BS(G_{1})+1$, $BS(G_{2}+e)=BS(G_{2})+n-1$.     

一类线图的带宽

本文给出了一类线图的带宽,并给出了它的最佳编号。     

关于奇强协调图的一些结果

对于一个(p,q)-图G,如果存在一个单射f:V(G)→{0,1,…,2q-1},使得边标号集合{f(uv)|uv∈E(G)}={1,3,5,…,2q-1},其中边标号为f(uv)=f(u)+f(v),那么称G是奇强协调图,并称f是G的一个奇强协调标号.通过研究若干奇强协调图,得出一些奇强协调图的性质.     

关于乘积图的二维带宽问题

给出一般乘积图的二维带宽的界，并解决一类乘积图的二维带宽问题．最后给出完全ｋ部图的二维带宽。     

单位球面上的一极值问题

设Ω是R~n中的紧集,1相似文献   

Extremal perfect graphs for a bound on the domination number

We examine classes of extremal graphs for the inequality γ(G)?|V|-max{d(v)+β_v(G)}, where γ(G) is the domination number of graph G, d(v) is the degree of vertex v, and β_v(G) is the size of a largest matching in the subgraph of G induced by the non-neighbours of v. This inequality improves on the classical upper bound |V|-maxd(v) due to Claude Berge. We give a characterization of the bipartite graphs and of the chordal graphs that achieve equality in the inequality. The characterization implies that the extremal bipartite graphs can be recognized in polynomial time, while the corresponding problem remains NP-complete for the extremal chordal graphs.     

图的割宽极值问题

The problem studied in this paper is to determine e(p, C), the minimum size of a connected graph G with given vertex number p and cut-width C.     

Existence of New Extremal Doubly-Even Codes and Extremal Singly-Even Codes

Recently the author and Kimura have considered a construction of doubly-even codes from a given doubly-even code. In this note, we show that the restricutoion of doubly-even can be removed in the above construction. As an application, at least 137 inequivalent extremal doubly-even [56,28,12] codes and at least 1000 inequivalent extremal doubly-even [40,20,8] codes are constructed from known self-dual codes. The existence of new extremal singly-even codes is also described.     

Spanning 3-colourable subgraphs of small bandwidth in dense graphs

A conjecture by Bollobás and Komlós states the following: For every γ>0 and integers r2 and Δ, there exists β>0 with the following property. If G is a sufficiently large graph with n vertices and minimum degree at least and H is an r-chromatic graph with n vertices, bandwidth at most βn and maximum degree at most Δ, then G contains a copy of H.This conjecture generalises several results concerning sufficient degree conditions for the containment of spanning subgraphs. We prove the conjecture for the case r=3.