剩余为几乎2-正则的6-圈系

Let Kn be a complete graph on n vertices. In this paper, we find the necessary conditions for the existence of a 6-cycle system of Kn - L for every nearly 2-regular leave L of Kn. This condition is also sufficient when the number of vertices of L is n - 4.     

3度图的最小顶点覆盖问题的多项式时间算法

最小顶点覆盖问题是图论和组合数学中经典的NP-Hard问题之一,在实际问题中有着广泛的应用.本文首先给出最小顶点覆盖问题的若干性质,然后根据这些性质设计了3度图最小顶点覆盖问题的一个多项式时间算法,并通过2个实例对算法进行了说明.     

给定围长的三圈图的无符号拉普拉斯谱半径

A tricyclic graph G =（V（G）, E（G）） is a connected and simple graph such that｜E（G）｜ = ｜V（G）｜＋2. Let Tg nbe the set of all tricyclic graphs on n vertices with girth g. In this paper, we will show that there exists the unique graph which has the largest signless Laplacian spectral radius among all tricyclic graphs with girth g containing exactly three（resp., four）cycles. And at the same time, we also give an upper bound of the signless Laplacian spectral radius and the extremal graph having the largest signless Laplacian spectral radius in Tg n,where g is even.     

含偶长圈的7点7边图的图设计

设λKν是ν阶λ重完全图，G是一个无孤立点的有限简单图,λKν的一个G-分拆(或G-设计，记为G-GDλ(ν))是指一个序偶(X，β)，其中X是完全图Kν的顶点集，β是Kν中同构于G的子图(称为区组)的族，使得Kν中每条边恰好出现在β的λ个区组中，本文完全解决了含偶长圈的十个7点7边图的图设计存在性问题。     

最大顶点覆盖问题的一种近似算法

给出了求解最大顶点覆盖问题的一种近似算法,讨论了它的性能保证,利用P ipage技术,为最大顶点覆盖问题设计出了0.75-近似算法.     

2-连通半无爪图的最长圈

A graph G is called quasi-claw-free if it satisfies the property:d(x,y)=2 there exists a vertex u∈N(x)∩N(y)such that N[u]■N[x]∪N[y].In this paper,we show that every 2-connected quasi-claw-free graph of order n with G■F contains a cycle of length at least min{3δ+2,n},where F is a family of graphs.     

基于最小权覆盖的医药电商配送中心选址及区域覆盖优化研究

配送中心选址及区域划分是物流配送过程中的关键环节,直接决定了配送时效及配送成本,在当今电子商务领域显得尤为重要。本文针对国内医药电商企业,提出了一种考虑药品配送时效的配送中心选址策略;随后建立该问题的整数规划模型,采用最小权顶点覆盖方法描述问题,并通过优先队列分支限界算法对此模型进行求解,得出最优选址结果;最后按最小运费原则将被重复覆盖区域进行再划分,得到配送中心选址及区域划分最终方案。本文基于上述策略为国内某头部医药电商企业提供了两种选址方案:保留企业原有配送中心并确定新配送中心选址点(改进选址方案)和从企业所有需求节点中重新为配送中心选址(重选址方案),并使用企业真实销量和物流数据进行算例分析。     

关于格点覆盖的一个注记

对于一个给定椭球,本文给出了它的任一全等椭球都包含一个整点的一个充分必要条件.     

基于AP聚类和集合覆盖模型的农电营业区域电费缴纳点选址研究

农电营业区域的电费缴纳点选址研究是解决用电客户缴费难、购电难的关键课题之一,而当前大数据环境为电费缴纳点的合理布局提供了一个新的研究思路.首先通过运用基于数据点间"消息传递"的AP聚类算法从大量用电客户中筛选出候选电费缴纳选址点,然后采用集合覆盖模型对候选电费缴纳选址点进行再优化,得到最优选址点.并以赤峰市宁城县居民电力缴费记录与低压数据明细为例,为实现"村村都有缴费点"的建设目标,对较少用电客户的台区进行最优电费缴纳点选址研究.在此基础上,对最优电费缴纳点选址下的供电营业厅资源配置进行了分析,为供电公司在农电营业区域电费缴纳点的选址布局提供决策支持.     

顶点覆盖约束下的同类机排序算法研究

给定m台同类机和n个工件,其中第j台机器的速度为s_j,第i个工件的加工时间为p_i并且在第j台机器上的负载为p_i/s_j.构造一个顶点赋权无向图G=(V,E;w),其中图G的n个顶点代表这n个工件,顶点权重代表相应工件的加工时间.本文研究顶点覆盖约束下的同类机排序问题.该问题是两个组合最优化问题的组合问题,其目标为首先确定图G的一个顶点覆盖,即图的一个顶点子集,使得图中每一条边都至少存在一个顶点属于该子集;然后把这个子集所代表的相应工件集放到m台同类机上加工,使得最大完工时间最小.该问题是NP-hard的.本文基于分层算法和LSPT算法设计一个■-近似算法,当所有机器的速度都相差不大时,该算法的近似效果较好.     

A 2-factor with Short Cycles Passing Through Specified Independent Vertices in Graph

For a graph G, we define σ₂(G) := min{d(u) + d(v)|u, v ≠ ∈ E(G), u ≠ v}. Let k ≥ 1 be an integer and G be a graph of order n ≥ 3k. We prove if σ₂(G) ≥ n + k − 1, then for any set of k independent vertices v ₁,...,v _k , G has k vertex-disjoint cycles C ₁,..., C _k of length at most four such that v _i ∈ V(C _i ) for all 1 ≤ i ≤ k. And show if σ₂(G) ≥ n + k − 1, then for any set of k independent vertices v ₁,...,v _k , G has k vertex-disjoint cycles C ₁,..., C _k such that v _i ∈ V(C _i ) for all 1 ≤ i ≤ k, V(C ₁) ∪...∪ V(C _k ) = V(G), and |C _i | ≤ 4 for all 1 ≤ i ≤ k − 1. The condition of degree sum σ₂(G) ≥ n + k − 1 is sharp. Received: December 20, 2006. Final version received: December 12, 2007.     

disjoint cycles containing specified independent vertices

Let k1 be an integer and G be a graph of order n3k satisfying the condition that σ₂(G)n+k-1. Let v₁,…,v_k be k independent vertices of G, and suppose that G has k vertex-disjoint triangles C₁,…,C_k with v_iV(C_i) for all 1ik.Then G has k vertex-disjoint cycles such that

(i) for all 1ik.

(ii) , and

(iii) At least k-1 of the k cycles are triangles.

The condition of degree sum σ₂(G)n+k-1 is sharp.

A note on Z 3-connected graphs with degree sum condition

A graph G satisfies the Ore-condition if d(x) + d(y) ≥ | V (G) | for any xy ■ E(G). Luo et al. [European J. Combin., 2008] characterized the simple Z3-connected graphs satisfying the Ore-condition. In this paper, we characterize the simple Z3-connected graphs G satisfying d(x) + d(y) ≥ | V (G) |-1 for any xy ■ E(G), which improves the results of Luo et al.     

A vertex cover with chorded 4-cycles

Let k be an integer with k ≥ 2 and G a graph with order n > 4k. We prove that if the minimum degree sum of any two nonadjacent vertices is at least n + k, then G contains a vertex cover with exactly k components such that k−1 of them are chorded 4-cycles. The degree condition is sharp in general.     

独立集的度和与图的哈密尔顿性

关于哈密尔顿连通图的一个基本结果是Ore给出的：设G是n阶图,若对于任意两个不相邻顶点u和v,有d(u) d(v)≥n 1,则G是哈密尔顿连通的．设G是一个图,对于任意u (?)V(G),令N(U)=∪_(u∈∪)N(u),d(U)=|N(U)|,称d(U)是U的度．本文利用独立集的度和得到如下结果：设s和t是正整数,G是(2s 2t 1)-连通n阶图．若对于任两个强不交独立集S,T,|S|=s,|T|=t,有d(S) d(T)≥n 1．则G是哈密尔顿连通的．同时也得到图的哈密尔顿性的其它相关结果．两个独立集S和T称为强不交的,如果S∪T也是独立集．