Star Chromatic Numbers of Planar Graphs

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

ON A CONJECTURE OF HARMONIOUS GRAPH

Let the coronas C_n⊙K_1 be the polygons with one additional end-point for eachvertex.Thom Grace conjectured that C_n⊙K_1 are harmonious for n even.In this paper,aproof of his conjecture is given.     

EQUITABLE COLORINGS OF LINE GRAPHS AND COMPLETE r-PARTITE GRAPHS

1. IntroductionLet G be a graph with vertex set V(G), edge set E(G), maximum degree A(G), minimumdegree 8(G), vertex chromatic number X(G), and edge chromatic number X'(G). G is equitablyk-colorable if V(G) can be pajrtitioned icao k independent sets VI, V2,'', Vk such that llKI III 1 5 1 for all i and j. The such smallest integer k as above is called the equitable chromaticnumber of G, denoted by X= (G). Similaxly we can define the equitable edge chromatic numberof a graph G and d…     

A FURTHER GENERALIZATION OF JUNG''''S THEOREM

Let G be a graph of order n. We define the distance between two vertices u andv in G, denoted by d(u, v), as the minimum value of the lengths of all u-v paths. We writeσ_k(G)=min{∑_i=1~k d(v_i)|{v_1, v_2,…, v_k} is an independent set in G} and NC2(G)=min {|N(u)∪N(v)| | d(u, v)=2}. We denote by ω(G) the number of components of agraph G. A graph G is called 1-tough if ω(G\S)≤|S| for every subset S of V(G) withω(G\S)>l. By c(G) we denote the length of the longest cycle in G; in particular, G iscalled a Hamiltonian graph if c(G)=n. H.A. Jung proved that every 1-tough graphwith order n≥11 and σ2≥n-4 is Hamiltonian. We generalize it further as follows: ifG is a 1-tough graph and σ3(G)≥n, then c(G)≥min {n,2NC2(G)+4}. Thus, theconjecture of D. Bauer, G. Fan and H.J. Veldman in [2] is completely solved.     

三种典型的基于图分割的谱聚类方法比较

在分析谱聚类实现思路和已有算法基础上,对规范切判据,最小最大切判据和自动确定聚类数目的谱聚类典型算法进行了研究和应用,通过理论分析算法各自实现机理的联系与区别,讨论它们各自的聚类特点,并利用UCI(University of California,Irvire)机器学习数据集试验对比了三种算法的聚类效果.发现谱聚类算法实现数据聚类的有效性,以及参数及相似度度量对算法性能有很大影响,在此基础上提出了算法用于解决可建模为模式识别的工程问题的可行思路,为工程实践提供了借鉴.     

THE NORMALITY OF CAYLEY GRAPHS OF SIMPLE GROUP A_5 WITH SMALL VALENCIES

1.IntroductionLetGbeafinitegroup.ForaCayleysubsetSofGnotcontainingtheidentityelement1,theCayley(di)graphX~Cay(G,S)ofGwithrespecttoSisdefinedasthedirectedgraphwithvertexsetV(X)=GandedgesetE(X)={(g,sg)IgEG,s6S}.IfS=S--',thentheadjacencyrelationissymmet...     

基于Spark的并行图聚类算法研究

对并行图聚类算法进行了研究。基于Spark 提出了一个新的并行图聚类算法；由于Spark 中的top 操作需要耗费大量的内存，提出了一个新算法来替代top 操作，有效减少了所消耗的内存；通过对自底向上的层次聚类算法进行改进提高了聚类的速度；基于图数据的特征提出了一种图数据过滤的方法来减少算法运行的时间以及所占用的空间并对其有效性进行了说明。仿真结果表明，运行效果优于进行比较的其他并行化图聚类算法。     

机场停机位分配问题的图着色模型及其算法

停机位分配作业关系到整个机场的系统运作,其作用相当重要。通过对停机位分配的分析,把停机位的分配转化为图着色,建立停机位分配问题的图着色模型,并引入时间片算法确定航班使用机位的时间冲突集合,根据"先到先服务"的原则给出了停机位分配的顶点序列着色算法,该算法的计算复杂性为O(n2k2),最后将该算法应用于一个算例。     

A Problem in Combinatorics

ＡＰｒｏｂｌｅｍｉｎＣｏｍｂｉｎａｔｏｒｉｃｓ￥ＨＵＪｉｕｒｅｎ（ＮａｎｋａｉＩｎｓｔｉｔｕｔｅｏｆＭａｔｈｅｍａｔｉｃｓＴｉａｎｊｉｎ３０００７１）Ａｂｓｔｒａｃｔ：Ｉｎｔｈｉｓｐａｐｅｒ，ｂｙｕｓｉｎｇａｎｏｖｅｌｍｅｔｈｏｄｏｆｇｒａｐｈ－ｃｏ...     

基于启发式策略的海量语义数据流划分算法研究

海量语义数据的剧烈增长对大数据分布式存储带来了巨大的挑战. 分布式存储的核心技术是图划分，论文介绍了基于图数据流划分的模型和分区启发函数策略，给出了针对RDF文件的图数据流划分算法和实现过程. 实验对几个真实RDF数据集进行划分，并与METIS （一种多层次的图划分算法）方法和哈希分区方法做了实验数据对比，验证了图数据流划分算法的有效性.     

FORBIDDEN SUBGRAPHS,DEGREES,NEIGHBORHOOD UNIONS AND CIRCUMFERENCES OF GRAPHS

Combining forbidden subgraphs with degree restrictions and neighborhood unionrestrictions,respectively,we prove the following results:(1) Let G be a 2-connected graph of order n,and 3≤c≤n.If for each induced subgraphL of order four of G(?)|V_1(L)∩S_c|≥2 if L≌K_(1,3),and |V(L)∩S_c|≥1 if L≌P_4,then thecircumference of G is at least c,where V_1(L)is the set of vertices with degree 1 of L,S_c isthe set of vertices with degree at least c/2 of G and P_4 is a path of order 4.(2) Let G be a 2-connected graph of order n,and n≥s+2.If for each induced subgraphL of G isomorphic to K_(1,3)or P_4,d_L(u,v)=2(?)|N(u)∪N(v)|≥s,then the circumferencec (G) of G is at least s+2.Moreover,if n≥s+3 and s is odd,then c(G)≥s+3.     

3D multipath planning for UAV based on network graph

According to the characteristic and the requirement of multipath planning,a new multipath planning method is proposed based on network.This method includes two steps:the construction of network and multipath searching.The construction of network proceeds in three phases:the skeleton extraction of the configuration space,the judgment of the cross points in the skeleton and how to link the cross points to form a network.Multipath searching makes use of the network and iterative penalty method (IPM) to plan multi-paths,and adjusts the planar paths to satisfy the requirement of maneuverability of unmanned aerial vehicle (UAV).In addition,a new height planning method is proposed to deal with the height planning of 3D route.The proposed algorithm can find multiple paths automatically according to distribution of terrain and threat areas with high efficiency.The height planning can make 3D route following the terrain.The simulation experiment illustrates the feasibility of the proposed method.     

A Degree Condition on Long Paths and Large Cycles

We present a new condition ensuring the existence of a large cycle of passing throughgiven edge.Let l(C)denote the length of the cycle C.Suppose G is a 4-connected graph withvertices set{x_1,x_2….x_n}and edge set E and with the property that,for any two positiveintegers j and k,j相似文献   

A k-HAMILTON-NICE SEQUENCE

Ａｋ－ＨＡＭＩＬＴＯＮ－ＮＩＣＥＳＥＱＵＥＮＣＥＬＩＵＹｉｐｉｎｇ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＮａｎｊｉｎｇＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，Ｎａｎｊｉｎｇ２１００２４，Ｃｈｉｎａ）ＴＩＡＮＦｅｎｇ（ＩｎｓｔｉｔｕｔｅｏｆＳｙｓ...     

图论中的DNA计算模型

基于生化反应机理的DNA计算模型受到科学领域内许多不同学科学者们的关注。DNA计算已经形成国际科学前沿领域内研究的一个新的热点。主要介绍了近几年国内关于图论的DNA计算模型研究的现状及研究进展。分析了图论的DNA计算模型中存在的问题。指出未来国内DNA计算研究的重点可以在三个方面:解的检测,降低空间复杂度,生化实验研究。     

分布式环境下多任务调度问题的分析与求解

将约束条件归纳为任务约束、链路约束和资源约束,在允许任务复制的情况下,建立了问题的约束与目标的完整数学模型;提出了一种基于任务复制的模拟人类社会中关系演化过程的簇调度算法IREA,包括前沿调度、动态分簇和分离图三个子算法.IREA采用全新的优先级规则,定义了关系数、依赖度、归并度等表示簇的优先级.通过对两个经典算例的计算,发现IREA能求出比算例所在文献算法所得解更优的解;对MJD算例,还得到了一个不同于原文献所给理论最优格局的一个新的最优格局.     

An Algorithm on Edge Partition

1　BackgroudWhenacarisinaccidentonroad,itmustbepulledawaytoavoidserioustrafficjamandnewaccidentshappening.Inoneroadnet,ifacarforcleaningbarsisaskedtogettotheplace,duringashortspanoftimedemanded,whereaccidenttookplace,howmanyclearbarsStationsshouldbesetup?andwhereshouldtheybe?Weresolvedtheproblemwiththemethodofgraph.Aroadnetcorrespondstoadefinitegraph,inwhichavertexdenotesanoriginoraterminusofaroad,anedgedenotesaroadandaweightofanedgedenotesalengthofaroad.Therefore,theabove-mentionedproblemcan…     

Application of rough graph in relationship mining

Based on the definition of class shortest path in weighted rough graph, class shortest path algorithm in weighted rough graph is presented, which extends classical shortest path algorithm. The application in relationship mining shows effectiveness of it.     

军事系统工程中的知识图谱应用及研究

目前随着通用知识图谱构建技术的发展、自然语言处理技术的进步以及各个行业挖掘数据深层关系的需要, 军事同电商、金融证券、医疗等行业一样, 也需要构建属于自己领域的知识图谱。通过定义军事知识图谱以及明确军事知识图谱使用时的特殊性, 总结了构建过程中的难点, 介绍了当前构建军事知识图谱的思路以及使用的技术手段, 汇总了军事领域应用知识图谱的现状。最后, 给出了知识图谱最新的研究进展, 并针对军事领域知识图谱中一部分未解决的困难问题提供了一种可能的解决思路。     

Application of rough graph in relationship mining

Based on the definition of class shortest path in weighted rough graph,class shortest path algorithm in weighted rough graph is presented,which extends classical shortest path algorithm.The application in relationship mining shows effectiveness of it.