EDGE RECONSTRUCTION OF PLANAR GRAPHS WITH MINIMUM DEGREE AT LEAST THREE-(Ⅲ)

ＥＤＧＥＲＥＣＯＮＳＴＲＵＣＴＩＯＮＯＦＰＬＡＮＡＲＧＲＡＰＨＳＷＩＴＨＭＩＮＩＭＵＭＤＥＧＲＥＥＡＴＬＥＡＳＴＴＨＲＥＥ－（Ⅲ）￥ＦＡＮＨｏｎｇｂｉｎｇ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＳｈａｎｄｏｎｇＵｎｉｖｅｒｓｉｔｇ，Ｊｉｎａ...     

EDGE RECONSTRUCTION OF PLANAR GRAPHS WITH MINIMUM DEGREE AT LEAST THREE-(Ⅰ)

The object of this series of papers is to show that every planar graph ofminimum degree at least 3 is edge reconstructible. In this paper, we prove that such agraph with connectivity 2 is edge reconstructible.     

EDGE RECONSTRUCTION OF PLANAR GRAPHS WITH MINIMUM DEGREE AT LEAST THREE-(Ⅱ)

ＥＤＧＥＲＥＣＯＮＳＴＲＵＣＴＩＯＮＯＦＰＬＡＮＡＲＧＲＡＰＨＳＷＩＴＨＭＩＮＩＭＵＭＤＥＧＲＥＥＡＴＬＥＡＳＴＴＨＲＥＥ－（Ⅱ）￥ＦＡＮＨｏｎｇｂｉｎｇ（ＤｅｐｏｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＳｈａｎｄｏｎｇＵｎｉｖｅｒｓｉｔｙ，Ｊｉｎａ...     

PANCONNECTIVITY AND 2-CONNECTED CLAW-FREE GRAPHS

ＰＡＮＣＯＮＮＥＣＴＩＶＩＴＹＡＮＤ２－ＣＯＮＮＥＣＴＥＤＣＬＡＷ－ＦＲＥＥＧＲＡＰＨＳ￥ＧＡＯＪｉｎｇｚｈｅｎ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＳｈａｄｄｏｃｋＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，Ｊｉｎａｎ２５００１４，Ｃｈｉｎａ）Ｚ...     

Forbidden Subgraphs, Distance,and Hamiltonicity

ＦｏｒｂｉｄｄｅｎＳｕｂｇｒａｐｈｓ，Ｄｉｓｔａｎｃｅ，ａｎｄＨａｍｉｌｔｏｎｉｃｉｔｙＨＵＺｈｉｑｕａｎＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＨｕａｚｈｏｎｇＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，Ｗｕｈａｎ４３００７０Ａｂｓｔｒａｃｔ：Ａｇｒ...     

THE CONNECTIVITY OF MAXIMUM MATCHING GRAPHS

The maximum matching graph of a graph has a vertex for each maximummatching and an edge for each pair of maximum matchings which differ by exactly oneedge. In this paper, we prove that the connectivity of maximum matching graph of abipartite graph is equal to its minimum degree.     

HAJóS'''' CONJECTURE AND CONNECTIVITY OF EULERIAN GRAPHS

Hajos' conjecture asserts that a simple eulerian graph on n vertices can be decomposed into at most n-1/2 circuits. In this paper, we propose a new conjecture which is equivalent to Hajos' conjecture, and show that to prove Hajos' conjecture, it is sufficient to prove this new conjecture for 3-connected graphs. Furthermore, a special 3-cut is considered also.     

STRONG EMBEDDING OF HP-GRAPHS ON SURFACE WITH HIGHER GENUS

In 1990, Bondy posed the small circuit double cover （SCDC） conjecture： Every 2-connected graph has a circuit double cover （CDC） with the number of circuits less than ｜v｜ （the order of the vertex set V）. The strong embedding conjecture states that every 2-connected graph has a strong embedding on some surface in which the boundary of each face is a circuit. In this paper, HP-graph is defined as the graph which has a strong embedding on the projective plane with one face of valence ｜V｜ and the other faces of valence 3. And it is proved that the HP-graph has a strong embedding with ｜V｜ - 1 or less faces on some surface, which confirms both the SCDC conjecture and the strong embedding conjecture.     

Two Sufficient Conditions for Hamiltonian Graphs

ＴｗｏＳｕｆｆｉｃｉｅｎｔＣｏｎｄｉｔｉｏｎｓｆｏｒＨａｍｉｌｔｏｎｉａｎＧｒａｐｈｓＬＩＧｕｏｊｕｎ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＹａｎｔａｉＴｅａｃｈｅｒ＇ｓＣｏｌｌｅｇｅ，Ｙａｎｔａｉ２６４０００，Ｓｈａｎｄｏｎｇ）ＬＩＵＺ...     

无人飞行器Ad hoc网络中基于容错的中继节点配置

针对无人飞行器Ad hoc网络的容错设计需求,采用增加中继节点的方法实现。在二维平面同构网络中,将容错问题转化为边长受限条件下最少数量Steiner点的Steiner树问题。提出了两种基于最小成本子图的中继节点配置算法,以求解最少数量的中继节点及其位置,使改变后的网络拓扑图为顶点2-连通,实现容错。第一种为多项式时间的8-近似算法;第二种为随机近似算法,采用文化基因算法,搜索需要新增加的最小成本强化边组合。仿真结果表明了所提算法的有效性,当网络规模较小和中等时,随机近似算法得到的中继节点数量较少,平均情况下性能较优。     

A NEIGHBORHOOD UNION CONDITION FOR PANCYCLIC GRAPHS

1.IntroductionWeconsideronlysimplefinitegraphs.OurbasicnotationandterminologynotdefinedherefollowthOSeofBondyandMurtyll].ForagraphG,letV(G)andE(G)(orjustVandE)deDOtelievertexsetandedgeset,respectively.Wedenoteapathandacyclecontaining8veniCesbyPaandCarespectively.ThecycleCaiscalledans-cycle.Denotebyg(G)(orbrieflybyg)thegirthofG1.SetNC=min{IN(u)UN(v)l:tv相似文献   

爪心独立图的可扩圈

图Ｇ中的一个与Ｋ１，３同构的导出子图叫做Ｇ的一个爪。爪中的３次顶点叫该爪的爪心。Ｂ表示Ｇ中所有爪心构成的集合。本文将证明：设Ｇ是顶点数≥３的连通、局部连通图，如果Ｇ的爪心集合Ｂ是点独立集，且Ｇ－Ｂ是局部连通的，则Ｇ是完全圈可扩的。     

ON THE INVERSE MINIMUM SPANNING TREE PROBLEM WITH MINIMUM NUMBER OF PERTURBED EDGES

Let G=be a network with the vertex set V,the edge set E and the length vector L, andlet T~* be a prior determined spanning tree of G. The inverse minimum spanning tree problem withminimum number of perturbed edges is to perturb the length vector L to L+δ, such that T~* is one ofminimum spanning trees under the length vector L+δ and the number of perturbed edges is minimum.This paper establishes a mathematical model for this problem and transforms it into a minimumvertex covering problem in a bipartite graph G_0, a path-graph. Thus a strongly polynomial algorithmwith time complexity O(mn~2) can be designed by using Hungarian method.     

HAMILTONICITY IN 2-CONNECTED {K_(1,3) F}-FREE GRAPHS

ＨＡＭＩＬＴＯＮＩＣＩＴＹＩＮ２－ＣＯＮＮＥＣＴＥＤ｛Ｋ_（１，３）Ｆ｝－ＦＲＥＥＧＲＡＰＨＳ￥ＬＩＧｕｏｊｕｎ（ＭａｔｈｅｍａｔｉｃｓＤｅｐｅｒｔｍｅｎｔｏｆＹａｎｔａｉＴｅａｃｈｅｒ＇ｓＣｏｌｌｅｇｅ，Ｙａｎｔａｉ２６４０００，Ｃｈｉｎａ）ＬＩＵ?..     

利用灰色理论构造统计量进行图像边缘检测

提出了基于灰色绝对关联度构造统计量进行图像边缘检测的新算法。所提算法将像素8邻域按水平、垂直方向分为4个部分,再按两对角线方向分为另外4个部分,基于灰色绝对关联度模型构造一种统计量,分别计算8个部分内像素的统计值,取最小的统计值与阈值比较,从而确定邻域中心像素是否为边缘点及其边缘方向。实验表明,所提算法简单、易实现,具有一定抗噪性能及检测边缘准确清晰等优点,对于灰度变化剧烈的图像检测出的边缘效果比传统算法要好。     

子任务调度和时延联合优化的MEC卸载方案

移动边缘计算(mobile edge computing, MEC)为5G超低时延业务提供了解决方案。如何设计低时延、高效率的任务卸载方案,是MEC面临的主要难题之一。为此,针对端-边协同MEC服务场景,研究了大型计算任务的低时延、低能耗部分卸载方案,通过将用户任务划分为多个有顺序依赖关系的子任务并构建子任务的有向无环关系图,设计了能够最小化卸载时延的子任务调度方案,提出了基于任务复制的最早卸载执行算法,解决了能耗受限下的任务最小时延卸载计算。仿真结果表明,提出的MEC卸载方案能够有效减少任务处理时延,降低系统能耗。     

VERTEX-DISJOINT QUADRILATERALS IN BIPARTITE GRAPHS

H. Wang considered the minimum degrees condition that G has large vertex-disjoint cycles in bipartite graphs. Motivated by this, we consider the small vertex-disjoint cycles in bipartite graphs in this paper. We prove the following result: Let m > 3, n > 2 and k >1 be three integers. Let G = (V1,V2;E) be a bipartite graph with | V1| = | V2| =n > 2k 1. If the minimum degreefor any cycle C of G with length 2m, then G contains k vertex-disjoint cycles of length 4. Moreover, the degrees condition is sharp.     

Star Chromatic Numbers of Planar Graphs

１ＩｎｔｒｏｄｕｃｔｉｏｎＤｅｆｉｎｉｔｉｏｎ１．１Ｌｅｔｋ,ｄｂｅｎａｔｕｒａｌｎｕｍｂｅｒｓｓｕｃｈｔｈａｔｋ２ｄ,ａ（ｋ,ｄ）－ｃｏｌｏｒｉｎｇｏｆａｇｒａｐｈＧ＝（Ｖ,Ｅ）ｉｓａｍａｐｐｉｎｇｃ：Ｖ→Ｚｋ,ｓｕｃｈｔｈａｔｆｏｒｅａｃｈｅｄ...     

基于MEC的任务卸载和资源分配联合优化方案

面对时延敏感度不同的多种用户,如何有效利用频谱资源和计算资源受限的边缘节点来保障其时延能耗需求成为关键问题。为此,提出了基于移动边缘计算(mobile edge computing, MEC)的任务卸载和资源分配联合优化方案。首先,为最小化卸载任务在MEC的总计算时间,给每个用户分配最优的MEC计算资源。其次,基于时延敏感度、用户满意度和资源块(resource block, RB)质量,引入RB分配算法,以分布式执行。最后,用户通过比较本地计算开销和卸载计算开销做出卸载决策。仿真结果表明，所提算法在满足高时延敏感用户的需求前提下,通过有效地分配传输资源和计算资源,实现了最小的系统开销。