直径不超过4的树的割宽

§ 1　IntroductionThe cutwidth problem for graphs,as well as a class of optimal labeling and embed-ding problems,have significant applications in VLSI designs,network communicationsand other areas (see [2 ] ) .We shall follow the graph-theoretic terminology and notation of [1 ] .Let G=(V,E)be a simple graph with vertex set V,| V| =n,and edge set E.A labeling of G is a bijec-tion f:V→ { 1 ,2 ,...,n} ,which can by regarded as an embedding of G into a path Pn.Fora given labeling f of G,th…     

单圈图的最大特征值序

主要讨论了单圈图按其最大特征值进行排序的问题，确定了该序的前六个图。     

最大2-正则诱导子图的长度

设G是2-连通图，c(G)是图G的最长诱导圈的长度，c′(G)是图G的最长诱导2-正则子图的长度。本文我们用图的特征值给出了c(G)和c′(G)的几个上界。     

Results of the maximum genus of graphs

In this paper,we provide a new class of up-embeddable graphs,and obtain a tight lower bound on the maximum genus of a class of 2-connected pseudographs of diameter 2 and of a class of diameter 4 multi-graphs.This extends a result of Skoviera.     

强色指数的一个新的上界

给出了图的强色指数的一个新的上界，并指出几类恰好达到该上界的图，从而改进了Erodoes和Nesetri的强色指数猜想，在某种意义上证明了这个猜想。     

带息力更新风险模型的一个极值分布

本文讨论了带息力的更新风险模型,得到了破产前最大盈余分布的递推公式,且在此基础上还给出了它满足的积分方程.     

Fully-angular polyhex chains with minimal total π-electron energy

By Hückel molecular orbital (HMO) theory, the calculation of the total energy of all π-electrons in conjugated hydrocarbons can be reduced to that of E(G)=|λ₁|+|λ₂|+?+|λn|, where λi are the eigenvalues of the corresponding graph G. Denote by Ψn the set of all fully-angular polyhex chains with n hexagons. In this paper, we show that Hn has the minimum total π-electron energy among chains in Ψn, where Hn is the helicene chain.     

Diameter graphs of polygons and the proof of a conjecture of Graham

We show that for an n-gon with unit diameter to have maximum area, its diameter graph must contain a cycle, and we derive an isodiametric theorem for such n-gons in terms of the length of the cycle. We then apply this theorem to prove Graham's 1975 conjecture that the diameter graph of a maximal 2m-gon (m?3) must be a cycle of length 2m−1 with one additional edge attached to it.     

Sufficient optimality conditions and duality in vector optimization with invex-convexlike functions

We prove the Kuhn-Tucker sufficient optimality condition, the Wolfe duality, and a modified Mond-Weir duality for vector optimization problems involving various types of invex-convexlike functions. The class of such functins contains many known generalized convex functions. As applications, we demonstrate that, under invex-convexlikeness assumptions, the Pontryagin maximum principle is a sufficient optimality condition for cooperative differential games. The Wolfe duality is established for these games.The author is indebted to the referees and Professor W. Stadler for valuable remarks and comments, which have been used to revise considerably the paper.