Halin图和Series-Parallel图的动态色数

图的动态着色是Bruce Montgomery于2001年引入的一个新概念。本文分别证明了Halin图和非5圈的Series—Parallel图的动态色数都不超过4。     

Scheduling algorithm based on critical tasks in heterogeneous environments

Heterogeneous computing is one effective method of high performance computing with many advantages. Task scheduling is a critical issue in heterogeneous environments as well as in homogeneous environments. A number of task scheduling algorithms for homogeneous environments have been proposed, whereas, a few for heterogeneous environments can be found in the literature. A novel task scheduling algorithm for heterogeneous environments, called the heterogeneous critical task （HCT） scheduling algorithm is presented. By means of the directed acyclic graph and the gantt graph, the HCT algorithm defines the critical task and the idle time slot. After determining the critical tasks of a given task, the HCT algorithm tentatively duplicates the critical tasks onto the processor that has the given task in the idle time slot, to reduce the start time of the given task. To compare the performance of the HCT algorithm with several recently proposed algorithms, a large set of randomly generated applications and the Gaussian elimination application are randomly generated. The experimental result has shown that the HCT algorithm outperforms the other algorithm.     

三角剖分图的色多项式

本文给出多项式f(λ)=(λ-i)(λ-j)[λ(λ-1)…(λq)],1≤i≤j≤是 q T-多项式的一个充分必要条件,并给出f(λ)=λ(λ-1)~(n_1)(λ-2)~(n_2)…(λ-q)~(n_q)是 T-多项式的一个必要条件,其中 q≥4.n_1,n_2,…,n_q 是正整数.     

Abel群上Cayley图的Hamilton圈分解的一点注记

本文证明了Alspach猜想当G(F,S)的度为5时也成立,并为从偶数度的情况导出奇数度的情况指出了一条可能的径途。     

关于图的bondage数的一点注记

对B. Hartnell关于图的bondage数的一个定理给出一个新的证明，并得到一些关于平面图的有用的结果.     

P_n~k和T_((k_1,k_2,…,k_n))的色多项式

本文研究了图Pnk和T(k1,k2,…,kn)的色多项式,得到P2n、P3n和T(k1,k2,…,kn)的色多项式递推公式,以及Pn2仅当n≤4时是色唯一图,T(k1,k2,…,kn)仅当n=1是色唯一图等结论.     

Lower Bound on de Bruijn Graphs Out-degree for Lower Traffic Load in Peer-to-peer Networks

Designers search for N-nodes peer-to-peer networks that can have O （1） out-degree with O （log2 N） average distance. Peer-to-peer schemes based on de Bruijn graphs are found to meet this requirement. By defining average load to evaluate the traffic load in a network, we show that in order to decrease the average load, the average distance of a network should decrease while the out-degree should increase. Especially, given out-degree k and N nodes, peer-to-peer schemes based on de Bruijn graphs have lower average load than other existing systems. The out-degree k of de Bruijn graphs should not be O（1） but should satisfy a lower bound described by an inequality κ^κ≥N^2, to ensure that the average load in peer-to-peer schemes based on de Bruijn graphs will not exceed that in Chord system.     

一个n-可扩图的局部交条件

设G是一个有偶数个顶点的连通图,α     

有向图的最长圈

讨论了有向简单图的最长图,并给出某些图的Hamilton路和Hamilton图的存在条件。