共查询到20条相似文献,搜索用时 140 毫秒
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Alavi等人定义了一种关于图的新分解,即“升分解”并且猜想,任何有正条边的简单图可升分解。Hung-LinFu曾证明恰有(n+1/2)条边的完全二分图可升分解。本文得到了一个中的结论,证明了具有任何条边的完全二分图都可升分解。 相似文献
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双随机矩阵有许多重要的应用,紧图族可以看作是组合矩阵论中关于双随机矩阵的著名的Birkhoff定理的拓广,具有重要的研究价值.确定一个图是否紧图是个困难的问题,目前已知的紧图族尚且不多,给出了三个结果:任意多个完全图的不交并是紧图;圈C_3与圈C_n(n3)的不交并是非紧图;当n是大于等于3的奇数时,完全图K_n与图K_(n+1)的不交并是非紧图,其中图K_(n+1)是从完全图K_(n+1)删去一因子而得到的图. 相似文献
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应用矩阵的初等变换得到了完全五部图的 Seidel 多项式,并给出了完全五部图是S-整图的一个充分必要条件。进一步刻画了完全正则五部图和两类特殊完全五部图的Seidel谱。 相似文献
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在他人研究完全多部图的邻接谱的基础上,对整完全多部图的Seidel多项式进行研究分析,以期得到完全六部图G是S-整图的充要条件.从讨论完全六部图的Seidel多项式入手,应用矩阵行初等变换的方法给出完全六部图G是S-整图的充要条件. 相似文献
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设G是去掉两条边的完全p-部图(p3),且是本质纽结图,经过有限次△-Y变换或点扩张得到图J.本文证明了,若从J中去掉任一顶点及与其相关联的所有边,则所得的图为一个本质链环图.这一结果给出了更多的本质纽结图满足Adams的纽结书中所提出的经典猜想"去掉本质纽结图的任一顶点得到的一定是本质链环图". 相似文献
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用P(G,λ)表示图G的色多项式.若对任意图H,当P(H,λ)=P(G,λ)时都有H和G同构,则称图G是色唯一的.给出了以下结果:m≥2且k≥0时,完全三部图K(m,m,m+k)是色唯一的;m≥2且m+1>k≥0时,完全三部图K(m,m+1,m+k)是色唯一的. 相似文献
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用P(G,λ)表示简单图G的色多项式.设G是一个给定的简单图,若对任意简单图H,当P(H,λ)=P(G,λ)时都有H和G同构(记为H≌G),则称图G是色唯一的.本文证明了以下结果:设n,k,△都为非负整数,其中k≥0,△∈{4,5},若n≥1/3k~2+1/3△~2-1/3k△-1/3k-1/3△+4/3,则完全三部图K(n,n+△,n+k)是色唯一的.同时还给出了一个猜想. 相似文献
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一个图G的区间图完全化问题包含两类子问题:侧廓问题和路宽问题,分别表示为P(G)和PW(G),其中侧廓问题是寻求G的一个边数最小的区间超图;路宽问题是寻求G的一个团数最小的区间超图.这两类子问题分别在数值代数、VLSI-设计和算法图论等学科领域中有重要的应用.对一般图来说,两类子问题都是NP-完全问题;但是对一些特殊图类来说,它们在多项式时间内可解.本文给出了树T的补图的具体侧廓和路宽值. 相似文献
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The interval graph completion problem on a graph G is to find an added edge set F such that G + F is an interval supergraph with the smallest possible number of edges. The problem has important applications to numerical algebra, V LSI-layout and algorithm graph theory etc; And it has been known to be N P-complete on general graphs. Some classes of special graphs have been investigated in the literatures. In this paper the interval graph completion problem on split graphs is investigated. 相似文献
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图G的弦图扩充问题包含两个问题:图G的最小填充问题和树宽问题,分别表示为f(G)和TW(G);图G的区间图扩充问题也包含两个问题:侧廓问题和路宽问题,分别表示为P(G)和PW(G).对一般图而言,它们都是NP-困难问题.一些特殊图类的填充数、树宽、侧廓问题和路宽具体值已被求出.主要研究树T的线图L(T)的弦图扩充问题;其次涉及到了两类特殊树—毛虫树和直径为4的树的线图的区间图扩充问题. 相似文献
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Amanda Montejano Alexandre Pinlou André Raspaud Éric Sopena 《Discrete Applied Mathematics》2010,158(12):1365-1379
In this paper, we study homomorphisms of 2-edge-colored graphs, that is graphs with edges colored with two colors. We consider various graph classes (outerplanar graphs, partial 2-trees, partial 3-trees, planar graphs) and the problem is to find, for each class, the smallest number of vertices of a 2-edge-colored graph H such that each graph of the considered class admits a homomorphism to H. 相似文献
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For a given graph G=(V,E), the interval completion problem of G is to find an edge set F such that the supergraph H=(V,E∪F) of G is an interval graph and |F| is minimum. It has been shown that it is equivalent to the minimum sum cut problem, the profile minimization problem and a kind of graph searching problems. Furthermore, it has applications in computational biology, archaeology, and clone fingerprinting. In this paper, we show that it is NP-complete on split graphs and propose an efficient algorithm on primitive starlike graphs. 相似文献
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图的扩张与稀疏矩阵计算中的若干优化问题 总被引:5,自引:1,他引:4
本文研究从稀疏矩阵计算中提出的若干离散最优化问题,即带宽,树宽,路宽,侧廓,扩充侧廓及填充问题。实际上,它们是一类图扩张问题;这些问题同时来源于各式各样的课题,如图子式理论,VLSI电路设计,互联网络及分子生物学等,本文从图论观点着重讨论两种统一途径:图的标号及图的扩张。 相似文献
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The authors recently defined a new graph invariant denoted by Ω(G) only in terms of a given degree sequence which is also related to the Euler characteristic. It has many important combinatorial applications in graph theory and gives direct information compared to the better known Euler characteristic on the realizability, connectedness, cyclicness, components, chords, loops etc. Many similar classification problems can be solved by means of Ω. All graphs G so that Ω(G) ≤-4 are shown to be disconnected, and if Ω(G) ≥-2, then the graph is potentially connected. It is also shown that if the realization is a connected graph and Ω(G) =-2, then certainly the graph should be a tree.Similarly, it is shown that if the realization is a connected graph G and Ω(G) ≥ 0, then certainly the graph should be cyclic. Also, when Ω(G) ≤-4, the components of the disconnected graph could not all be cyclic and if all the components of G are cyclic, then Ω(G) ≥ 0. In this paper, we study an extremal problem regarding graphs. We find the maximum number of loops for three possible classes of graphs.We also state a result giving the maximum number of components amongst all possible realizations of a given degree sequence. 相似文献