共查询到17条相似文献,搜索用时 140 毫秒
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图的树宽的结构性结果 总被引:6,自引:0,他引:6
图G的树宽是使得G成为一个k-树的子图的最小整数k.树宽的算法性结果在图子式理论及有关领域中已有深入的研究.本文着重讨论其结构性结果,包括拓扑不变性、子式单调性、可分解性、刻画问题、与其它参数的关系及由此引伸出的性质. 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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李红燕 《纯粹数学与应用数学》2016,32(2):127-131
连通图G的一个k-树是指图G的一个最大度至多是k的生成树.对于连通图G来说,其毁裂度定义为r(G)=max{ω(G-X)-|X|-m(G-X)|X■V(G),ω(G-X)1}其中ω(G-X)和m(G-X)分别表示G-X中的分支数目和最大分支的阶数.本文结合毁裂度给出连通图G包含一个k-树的充分条件;利用图的结构性质和毁裂度的关系逐步刻画并给出图G包含一个k-树的毁裂度条件. 相似文献
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第三讲图中之图这一讲准备进一步谈谈图的支撑子图.第一讲中我们提到了支撑树,第二讲中讲了支撑圈,现在我们所关心的是满足某种次(Yalency)条件的支撑子图.图G的一个子图被称为G的一个k-因子,如果它是k-价 相似文献
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关于k—消去图的若干新结果 总被引:2,自引:0,他引:2
汪长平 《数学物理学报(A辑)》1998,18(3):302-309
设G是一个图.k是自然数.图G的一个k-正则支撑子图称为G的一个k-因子.若对于G的每条边e.G—e都存在一个k-因子,则称G是一个k-消去图.该文得到了一个图是k-消去图的若干充分条件,推广了文[2—4]中有关结论. 相似文献
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Acta Mathematicae Applicatae Sinica, English Series - A k-tree is a tree with maximum degree at most k. In this paper, we give a sharp degree sum condition for a graph to have a spanning k-tree in... 相似文献
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Aung Kyaw 《Graphs and Combinatorics》2001,17(1):113-121
A k-tree of a connected graph is a spanning tree with maximum degree at most k. We obtain a sufficient condition for a graph
to have a k-tree, as a generalization of the condition of E. Flandrin, H. A. Jung and H. Li [3] for traceability. We also
extend early results of Y. Caro, I. Krasikov and Y. Roditty [2] and Min Aung and Aung Kyaw [4] for the maximal order of a
tree with bounded maximum degree in a graph.
Received: July 28, 1997 Final version received: April 13, 1998 相似文献
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In recent articles by Grohe and Marx, the treewidth of the line graph of a complete graph is a critical example—in a certain sense, every graph with large treewidth “contains” . However, the treewidth of was not determined exactly. We determine the exact treewidth of the line graph of a complete graph. 相似文献
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In 1977, Trotter and Moore proved that a poset has dimension at most 3 whenever its cover graph is a forest, or equivalently, has treewidth at most 1. On the other hand, a well-known construction of Kelly shows that there are posets of arbitrarily large dimension whose cover graphs have treewidth 3. In this paper we focus on the boundary case of treewidth 2. It was recently shown that the dimension is bounded if the cover graph is outerplanar (Felsner, Trotter, and Wiechert) or if it has pathwidth 2 (Biró, Keller, and Young). This can be interpreted as evidence that the dimension should be bounded more generally when the cover graph has treewidth 2. We show that it is indeed the case: Every such poset has dimension at most 1276. 相似文献
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The class of planar graphs has unbounded treewidth, since the k×k grid, ∀k∈N, is planar and has treewidth k. So, it is of interest to determine subclasses of planar graphs which have bounded treewidth. In this paper, we show that if G is an even-hole-free planar graph, then it does not contain a 9×9 grid minor. As a result, we have that even-hole-free planar graphs have treewidth at most 49. 相似文献
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《Operations Research Letters》2020,48(3):217-224
We investigate the complexity of local search based on steepest ascent. We show that even when all variables have domains of size two and the underlying constraint graph of variable interactions has bounded treewidth (in our construction, treewidth 7), there are fitness landscapes for which an exponential number of steps may be required to reach a local optimum. This is an improvement on prior recursive constructions of long steepest ascents, which we prove to need constraint graphs of unbounded treewidth. 相似文献
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Lorenzo Traldi 《Discrete Applied Mathematics》2006,154(6):1032-1036
We observe that a formula given by Negami [Polynomial invariants of graphs, Trans. Amer. Math. Soc. 299 (1987) 601-622] for the Tutte polynomial of a k-sum of two graphs generalizes to a colored Tutte polynomial. Consequently, an algorithm of Andrzejak [An algorithm for the Tutte polynomials of graphs of bounded treewidth, Discrete Math. 190 (1998) 39-54] may be directly adapted to compute the colored Tutte polynomial of a graph of bounded treewidth in polynomial time. This result has also been proven by Makowsky [Colored Tutte polynomials and Kauffman brackets for graphs of bounded tree width, Discrete Appl. Math. 145 (2005) 276-290], using a different algorithm based on logical techniques. 相似文献