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The Rupture Degree of Graphs with k-Tree 被引量:1
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作者 Yinkui Li Qingning Wang Xiaoling Wang 《Open Journal of Discrete Mathematics》 2016年第2期105-107,共3页
A k-tree of a connected graph G is a spanning tree with maximum degree at most k. The rupture degree for a connected graph G is defined by , where and , respectively, denote the order of the largest component and numb... A k-tree of a connected graph G is a spanning tree with maximum degree at most k. The rupture degree for a connected graph G is defined by , where and , respectively, denote the order of the largest component and number of components in . In this paper, we show that for a connected graph G, if  for any cut-set , then G has a k-tree. 展开更多
关键词 The Rupture Degree k-tree Induced Graph
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THE BANDWIDTH OF THE COMPLEMENT OF A K-TREE
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作者 YUAN JINJIANG AND LIN YIXUN 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 1998年第4期451-454,共4页
Abstract The paper proves that if G is a k tree, then the bandwidth B(G) of the complement G of G is given by B(G)=n-k-1, when GK k+K n-k , n-k-2, otherwise.
关键词 BANDWIDTH k-tree COMPLEMENT
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有界树宽的贝叶斯网络结构近似学习研究进展 被引量:1
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作者 王慧玲 綦小龙 《伊犁师范学院学报(自然科学版)》 2018年第1期62-66,共5页
概率图模型在机器学习和决策论尤其是不确定性领域中作用日益突出,如果能够有效地使用模型的表示、推断、学习等能力,可以建立适应不同问题域的智能系统.贝叶斯网络是这些模型使用最广泛的一类,由于其学习和推断的复杂性,近几年,从数据... 概率图模型在机器学习和决策论尤其是不确定性领域中作用日益突出,如果能够有效地使用模型的表示、推断、学习等能力,可以建立适应不同问题域的智能系统.贝叶斯网络是这些模型使用最广泛的一类,由于其学习和推断的复杂性,近几年,从数据中学习有界树宽的贝叶斯网络结构引起了研究者广泛关注.就目前有界树宽的贝叶斯网络结构近似学习技术做了深入的探讨并且归纳了有界树宽的贝叶斯网络结构学习亟待解决的两个问题. 展开更多
关键词 贝叶斯网络结构 有界树宽 k-tree
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基于Dandelion编码生成有界树宽CP-nets
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作者 李丛丛 刘惊雷 《计算机应用》 CSCD 北大核心 2021年第1期112-120,共9页
针对条件偏好网络(CP-nets)图模型在进行推理运算时的高时间复杂度的问题,提出了一种基于Dandelion编码生成有界树宽的CP-nets(BTW-CP-nets Gen)算法。首先,通过Dandelion编码与树宽为k的树结构(ktree)之间的双向映射原理推导出Dandelio... 针对条件偏好网络(CP-nets)图模型在进行推理运算时的高时间复杂度的问题,提出了一种基于Dandelion编码生成有界树宽的CP-nets(BTW-CP-nets Gen)算法。首先,通过Dandelion编码与树宽为k的树结构(ktree)之间的双向映射原理推导出Dandelion编码与k-tree之间的解码与编码算法,实现编码与树结构的一对一映射;其次,利用k-tree来约束CP-nets结构的树宽,并利用k-tree的特征树得到了CP-nets的有向无环图结构;最后,利用离散多值函数的双射计算出各CP-nets结构节点的条件偏好表,然后针对生成的有界树宽CP-nets进行占优查询检测。理论分析和实验数据表明,与Pruffer编码生成k-tree(Pruffer code)算法相比,BTW-CP-nets Gen算法的运行时间在生成简单结构和复杂结构时的下降幅度分别为21.1%和30.5%;而BTW-CP-nets Gen算法所生成的图模型在进行占优查询时的节点遍历比在简单结构和复杂结构上分别提高了18.48%和29.03%。BTW-CP-nets Gen算法在更短的时间内,占优查询时遍历的节点率更高。可见,BTW-CP-nets Gen算法在图模型的推理中能够有效提高算法效率。 展开更多
关键词 有界树宽 k-tree Dandelion编码 条件偏好网络 均匀性
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Algorithm for Cost Non-preemptive Scheduling of Partial k-Trees
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作者 Yiming Li Zhiqian Ye Xiao Zhou 《Open Journal of Applied Sciences》 2012年第4期233-236,共4页
Let G be a graph, in which each vertex (job) v has a positive integer weight (processing time) p(v) and eachedge (u,v) represented that the pair of jobs u and v cannot be processed in the same slot. In this paper we a... Let G be a graph, in which each vertex (job) v has a positive integer weight (processing time) p(v) and eachedge (u,v) represented that the pair of jobs u and v cannot be processed in the same slot. In this paper we assume that every job is non-preemptive. Let C={1,2,...} be a color set. A multicoloring (scheduling) F of G is to assign each job v a set of p(v) consecutive positive integers (processing consecutive time slots) in C so that any pair of adjacent vertices receive disjoint sets. Such a multicoloring is called a non-preemptive scheduling. The cost non-preemptive scheduling problem is to find an optimal multicoloring of G. 展开更多
关键词 COLORING Non-preemptive scheduling PARTIAL k-tree
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On a Spanning K-tree Containing Specified Vertices in a Graph
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作者 Fei-fei SONG Zhi-quan HU 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2019年第4期919-923,共5页
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 which specified vertices have degree less than t, where 1≤t≤k.We denote ... 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 which specified vertices have degree less than t, where 1≤t≤k.We denote by σ_k(G) the minimum value of the degree sum of k independent vertices in a graph G. Let k≥2,s≥0 and 1≤t≤k be integers, and suppose G is an(s + 1)-connected graph with σ_k(G)≥|G|+(k-t)s-1.Then for any s specified vertices, G contains a spanning k-tree in which every specified vertex has degree at most t. This improves a result obtained by Matsuda and Matsumura. 展开更多
关键词 SPANNING tree k-tree (s + 1)-connected GRAPHS degree SUM condition specified VERTICES
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Edge-Tenacity in Graphs 被引量:1
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作者 王志平 任光 赵连昌 《Journal of Mathematical Research and Exposition》 CSCD 北大核心 2004年第3期405-410,共6页
The edge-tenacity of a graph G(V,E) is denned as min{(|S|+T(G-S))/ω(G-S):S(?)E(G)},where T(G ?S) and ω(G-S), respectively, denote the order of the largest component and the number of the components of G-S. This is a... The edge-tenacity of a graph G(V,E) is denned as min{(|S|+T(G-S))/ω(G-S):S(?)E(G)},where T(G ?S) and ω(G-S), respectively, denote the order of the largest component and the number of the components of G-S. This is a better parameter to measure the stability of a network G, as it takes into account both the quantity and the order of components of the graph G-S. In a previous work, we established a necessary and sufficient condition for a graph to be edge-tenacious. These results are applied to prove that K-trees are strictly edge-tenacious. A number of results are given on the relation of edge-tenacity and other parameters, such as the higher-order edge toughness and the edge-toughness. 展开更多
关键词 edge cut-sets strictly edge-tenacious graph k-trees higher-order edge toughness edge toughness.
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