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Note on 2-edge-colorings of complete graphs with small monochromatic k-connected subgraphs
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作者 JIN Ze-min WANG Yu-ling WEN Shi-li 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2014年第2期249-252,共4页
Bollobas and Gyarfas conjectured that for n 〉 4(k - 1) every 2-edge-coloring of Kn contains a monochromatic k-connected subgraph with at least n - 2k + 2 vertices. Liu, et al. proved that the conjecture holds when... Bollobas and Gyarfas conjectured that for n 〉 4(k - 1) every 2-edge-coloring of Kn contains a monochromatic k-connected subgraph with at least n - 2k + 2 vertices. Liu, et al. proved that the conjecture holds when n 〉 13k - 15. In this note, we characterize all the 2-edge-colorings of Kn where each monochromatic k-connected subgraph has at most n - 2k + 2 vertices for n ≥ 13k - 15. 展开更多
关键词 monochromatic subgraph k-connected subgraph 2-edge-coloring.
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Accurate querying of frequent subgraphs in power grid graph data 被引量:2
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作者 Aihua Zhou Lipeng Zhu +1 位作者 Xinxin Wu Hongbin Qiu 《Global Energy Interconnection》 2019年第1期78-84,共7页
With the development of information technology, the amount of power grid topology data has gradually increased. Therefore, accurate querying of this data has become particularly important. Several researchers have cho... With the development of information technology, the amount of power grid topology data has gradually increased. Therefore, accurate querying of this data has become particularly important. Several researchers have chosen different indexing methods in the filtering stage to obtain more optimized query results because currently there is no uniform and efficient indexing mechanism that achieves good query results. In the traditional algorithm, the hash table for index storage is prone to "collision" problems, which decrease the index construction efficiency. Aiming at the problem of quick index entry, based on the construction of frequent subgraph indexes, a method of serialized storage optimization based on multiple hash tables is proposed. This method mainly uses the exploration sequence to make the keywords evenly distributed; it avoids conflicts of the stored procedure and performs a quick search of the index. The proposed algorithm mainly adopts the "filterverify" mechanism; in the filtering stage, the index is first established offline, and then the frequent subgraphs are found using the "contains logic" rule to obtain the candidate set. Experimental results show that this method can reduce the time and scale of candidate set generation and improve query efficiency. 展开更多
关键词 POWER grid GRAPH database GRAPH computing Multi-Hash TABLE Frequent subgraphS
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ON THE ASCENDING SUBGRAPH DECOMPOSITIONS OF REGULAR GRAPHS
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作者 CHENHUAITANG MAKEJIE 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 1998年第2期165-170,共6页
The definition of the ascending subgraph decomposition was given by Alavi. It has been conjectured that every graph of positive size has an ascending subgraph decomposition. In this paper it is proved that the regular... The definition of the ascending subgraph decomposition was given by Alavi. It has been conjectured that every graph of positive size has an ascending subgraph decomposition. In this paper it is proved that the regular graphs under some conditions do have an ascending subgraph decomposition. 展开更多
关键词 Ascending subgraph decomposition regular graph induced subgraph
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Subgraph Matching Using Graph Neural Network 被引量:2
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作者 GnanaJothi Raja Baskararaja MeenaRani Sundaramoorthy Manickavasagam 《Journal of Intelligent Learning Systems and Applications》 2012年第4期274-278,共5页
Subgraph matching problem is identifying a target subgraph in a graph. Graph neural network (GNN) is an artificial neural network model which is capable of processing general types of graph structured data. A graph ma... Subgraph matching problem is identifying a target subgraph in a graph. Graph neural network (GNN) is an artificial neural network model which is capable of processing general types of graph structured data. A graph may contain many subgraphs isomorphic to a given target graph. In this paper GNN is modeled to identify a subgraph that matches the target graph along with its characteristics. The simulation results show that GNN is capable of identifying a target sub-graph in a graph. 展开更多
关键词 subgraph Matching GRAPH NEURAL NETWORK Backpropagation RECURRENT NEURAL NETWORK FEEDFORWARD NEURAL NETWORK
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k-Factors and Spanning Subgraph in Graphs
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作者 WANG Zhi-guo ZHANG Yi 《Chinese Quarterly Journal of Mathematics》 CSCD 北大核心 2006年第1期143-147,共5页
In this paper, we discussed k-factors and spanning subgraph, and propose a conjecture which will lead to a series of important conclusion.
关键词 K-FACTOR 2-connected graph spanning subgraph
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On the Ascending Subgraph Decomposition Problem
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作者 赵光锋 董会英 +1 位作者 王朝霞 徐付霞 《Chinese Quarterly Journal of Mathematics》 CSCD 1999年第2期52-58, ,共7页
Alavi and his fellows defined the concept of ascending subgraph decomposition of a graph and conjectured that every graph with positive size has an ascending subgraph decomposition in paper [1]. Paper [2] proved that ... Alavi and his fellows defined the concept of ascending subgraph decomposition of a graph and conjectured that every graph with positive size has an ascending subgraph decomposition in paper [1]. Paper [2] proved that K n-R n-1 has a star ascending subgraph decomposition,here K n is the complete graph with order n and R n-1 is a subgraph of K n with size at most n-1. In paper [3],Ma Kejie and Chen Huaitang proved that K n-R n has an ascending subgraph decomposition when the size of R n is not greater than n. In this paper we will prove K n-R has an ascending subgraph decomposition when the size of R is less than 3n/2. This paper will also give the concept of comet and prove that K n-R n-1 has a comet ascending subgraph decomposition. 展开更多
关键词 GRAPH COMET ascending subgraph decomposition CONJECTURE
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Inductive Relation Prediction by Disentangled Subgraph Structure
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作者 Guiduo Duan Rui Guo +2 位作者 Wenlong Luo Guangchun Luo Tianxi Huang 《Tsinghua Science and Technology》 SCIE EI CAS 2024年第5期1566-1579,共14页
Currently,most existing inductive relation prediction approaches are based on subgraph structures,with subgraph features extracted using graph neural networks to predict relations.However,subgraphs may contain disconn... Currently,most existing inductive relation prediction approaches are based on subgraph structures,with subgraph features extracted using graph neural networks to predict relations.However,subgraphs may contain disconnected regions,which usually represent different semantic ranges.Because not all semantic information about the regions is helpful in relation prediction,we propose a relation prediction model based on a disentangled subgraph structure and implement a feature updating approach based on relevant semantic aggregation.To indirectly achieve the disentangled subgraph structure from a semantic perspective,the mapping of entity features into different semantic spaces and the aggregation of related semantics on each semantic space are updated.The disentangled model can focus on features having higher semantic relevance in the prediction,thus addressing a problem with existing approaches,which ignore the semantic differences in different subgraph structures.Furthermore,using a gated recurrent neural network,this model enhances the features of entities by sorting them by distance and extracting the path information in the subgraphs.Experimentally,it is shown that when there are numerous disconnected regions in the subgraph,our model outperforms existing mainstream models in terms of both Area Under the Curve-Precision-Recall(AUC-PR)and Hits@10.Experiments prove that semantic differences in the knowledge graph can be effectively distinguished and verify the effectiveness of this method. 展开更多
关键词 disentangled subgraph structure knowledge graph completion Gated Recurrent Unit(GRU) feature updating
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A subgraph matching algorithm based on subgraph index for knowledge graph 被引量:1
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作者 Yunhao SUN Guanyu LI +2 位作者 Jingjing DU Bo NING Heng CHEN 《Frontiers of Computer Science》 SCIE EI CSCD 2022年第3期123-140,共18页
The problem of subgraph matching is one fundamental issue in graph search,which is NP-Complete problem.Recently,subgraph matching has become a popular research topic in the field of knowledge graph analysis,which has ... The problem of subgraph matching is one fundamental issue in graph search,which is NP-Complete problem.Recently,subgraph matching has become a popular research topic in the field of knowledge graph analysis,which has a wide range of applications including question answering and semantic search.In this paper,we study the problem of subgraph matching on knowledge graph.Specifically,given a query graph q and a data graph G,the problem of subgraph matching is to conduct all possible subgraph isomorphic mappings of q on G.Knowledge graph is formed as a directed labeled multi-graph having multiple edges between a pair of vertices and it has more dense semantic and structural features than general graph.To accelerate subgraph matching on knowledge graph,we propose a novel subgraph matching algorithm based on subgraph index for knowledge graph,called as FGqT-Match.The subgraph matching algorithm consists of two key designs.One design is a subgraph index of matching-driven flow graph(FGqT),which reduces redundant calculations in advance.Another design is a multi-label weight matrix,which evaluates a near-optimal matching tree for minimizing the intermediate candidates.With the aid of these two key designs,all subgraph isomorphic mappings are quickly conducted only by traversing FGqj.Extensive empirical studies on real and synthetic graphs demonstrate that our techniques outperform the state-of-the-art algorithms. 展开更多
关键词 knowledge graph subgraph matching subgraph index matching tree
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基于图重构和子图挖掘的僵尸网络检测方法
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作者 景永俊 吴悔 +1 位作者 陈旭 宋吉飞 《郑州大学学报(工学版)》 CAS 北大核心 2025年第1期34-41,共8页
针对伪装后僵尸网络主机难以检测的问题,提出一种基于图重构和子图挖掘的僵尸网络检测方法(GR-SGM)。首先,将网络数据转化为图数据,并对其进行重构以此增强主机节点特征表示;其次,基于重构图中拓扑结构、节点的特征和位置变化设计僵尸... 针对伪装后僵尸网络主机难以检测的问题,提出一种基于图重构和子图挖掘的僵尸网络检测方法(GR-SGM)。首先,将网络数据转化为图数据,并对其进行重构以此增强主机节点特征表示;其次,基于重构图中拓扑结构、节点的特征和位置变化设计僵尸网络子图评分函数,以此捕捉伪装后的特征,提取出僵尸网络子图,并对原始图和重构图进行预检测,以提高检测的准确率和效率,减少重构误差;最后,对预检测结果和僵尸网络子图进行综合评分,以获取完整的僵尸网络信息。在ISCX2014僵尸网络数据集和CICIDS2017僵尸网络数据集上的实验结果表明:GR-SGM的检测准确率分别达到99.98%和99.91%,F 1分别达到99.94%和99.65%,相较于其他僵尸网络检测模型,GR-SGM能更加高效准确地识别僵尸网络节点,同时具有更低的误报率。 展开更多
关键词 僵尸网络 子图挖掘 图重构 网络安全 预检测
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A matching algorithm between precursory 3D process model and 2D working procedure drawing based on subgraph isomorphism 被引量:4
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作者 HUANG Rui ZHANG ShuSheng +1 位作者 FAN HaiTao TAO Jun 《Science China(Technological Sciences)》 SCIE EI CAS 2011年第7期1826-1832,共7页
To meet the urgent requirement of enterprises for three-dimensional (3D) process models, an approach based on subgraph isomorphism is proposed to solve the matching problem between precursory 3D process model and 2D w... To meet the urgent requirement of enterprises for three-dimensional (3D) process models, an approach based on subgraph isomorphism is proposed to solve the matching problem between precursory 3D process model and 2D working procedure drawings. First, the projection drawings of the precursory 3D process model are obtained, then the primitives are extracted and the attributed adjacency graph (AAG) is constructed. Finally, by taking the 2D working procedure drawing as the AAG, and the projection drawing as the whole AAG, the matching problem between precursory 3D process model and 2D working procedure drawings is translated into the problem of subgraph isomorphism. To raise the matching efficiency, the AAG is partitioned, and the vertexes of the graph are classified effectively using the vertex’s attributes. Experimental results show that this method is able to support exact match and the matching efficiency can meet the requirement of practical applications. 展开更多
关键词 subgraph isomorphism process model three-dimensional model reconstruction working procedure drawing
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Extracting Semantic Subgraphs to Capture the Real Meanings of Ontology Elements 被引量:2
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作者 汪鹏 徐宝文 周毓明 《Tsinghua Science and Technology》 SCIE EI CAS 2010年第6期724-733,共10页
An element may have heterogeneous semantic interpretations in different ontologies. Therefore, understanding the real local meanings of elements is very useful for ontology operations such as querying and reasoning, w... An element may have heterogeneous semantic interpretations in different ontologies. Therefore, understanding the real local meanings of elements is very useful for ontology operations such as querying and reasoning, which are the foundations for many applications including semantic searching, ontology matching, and linked data analysis. However, since different ontologies have different preferences to describe their elements, obtaining the semantic context of an element is an open problem. A semantic subgraph was proposed to capture the real meanings of ontology elements. To extract the semantic subgraphs, a hybrid ontology graph is used to represent the semantic relations between elements. An extracting algorithm based on an electrical circuit model is then used with new conductivity calculation rules to improve the quality of the semantic subgraphs. The evaluation results show that the semantic subgraphs properly capture the local meanings of elements. Ontology matching based on semantic subgraphs also demonstrates that the semantic subgraph is a promising technique for ontology applications. 展开更多
关键词 ONTOLOGY ontology graph semantic subgraph ontology matching
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Using partial evaluation in holistic subgraph search 被引量:1
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作者 Peng PENG Lei ZOU +1 位作者 Zhenqin DU Dongyan ZHAO 《Frontiers of Computer Science》 SCIE EI CSCD 2018年第5期966-983,共18页
Because of its wide application, the subgraph matching problem has been studied extensively during the past decade. However, most existing solutions assume that a data graph is a vertex/edge-labeled graph (i.e., each... Because of its wide application, the subgraph matching problem has been studied extensively during the past decade. However, most existing solutions assume that a data graph is a vertex/edge-labeled graph (i.e., each vertex/edge has a simple label). These solutions build structural indices by considering the vertex labels. However, some real graphs contain rich-content vertices such as user profiles in social networks and HTML pages on the World Wide Web. In this study, we consider the problem of subgraph matching using a more general scenario. We build a structural index that does not depend on any vertex content. Based on the index, we design a holistic subgraph matching algorithm that considers the query graph as a whole and finds one match at a time. In order to further improve efficiency, we propose a "partial evaluation and assembly" framework to find sub- graph matches over large graphs. Last but not least, our index has light maintenance overhead. Therefore, our method can work well on dynamic graphs. Extensive experiments on real graphs show that our method outperforms the state-of-the-art algorithms. 展开更多
关键词 subgraph search holistic approach partial evaluation and assembly
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METHOD FOR QUICKLY INFERRING THE MECHANISMS OF LARGE-SCALE COMPLEX NETWORKS BASED ON THE CENSUS OF SUBGRAPH CONCENTRATIONS 被引量:1
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作者 Bo YANG Xiaorong CHEN 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2009年第2期252-259,共8页
A Mechanism-Inferring method of networks exploited from machine learning theory caneffectively evaluate the predicting performance of a network model.The existing method for inferringnetwork mechanisms based on a cens... A Mechanism-Inferring method of networks exploited from machine learning theory caneffectively evaluate the predicting performance of a network model.The existing method for inferringnetwork mechanisms based on a census of subgraph numbers has some drawbacks,especially the needfor a runtime increasing strongly with network size and network density.In this paper,an improvedmethod has been proposed by introducing a census algorithm of subgraph concentrations.Networkmechanism can be quickly inferred by the new method even though the network has large scale andhigh density.Therefore,the application perspective of mechanism-inferring method has been extendedinto the wider fields of large-scale complex networks.By applying the new method to a case of proteininteraction network,the authors obtain the same inferring result as the existing method,which approvesthe effectiveness of the method. 展开更多
关键词 Large-scale complex networks mechanism-inferring model evaluation subgraph census.
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MF-SuP-pK_(a): Multi-fidelity modeling with subgraph pooling mechanism for pK_(a) prediction 被引量:1
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作者 Jialu Wu Yue Wan +4 位作者 Zhenxing Wu Shengyu Zhang Dongsheng Cao Chang-Yu Hsieh Tingjun Hou 《Acta Pharmaceutica Sinica B》 SCIE CAS CSCD 2023年第6期2572-2584,共13页
Acid-base dissociation constant(pK_(a)) is a key physicochemical parameter in chemical science, especially in organic synthesis and drug discovery. Current methodologies for pK_(a) prediction still suffer from limited... Acid-base dissociation constant(pK_(a)) is a key physicochemical parameter in chemical science, especially in organic synthesis and drug discovery. Current methodologies for pK_(a) prediction still suffer from limited applicability domain and lack of chemical insight. Here we present MF-SuP-pK_(a)(multi-fidelity modeling with subgraph pooling for pK_(a) prediction), a novel pK_(a) prediction model that utilizes subgraph pooling, multi-fidelity learning and data augmentation. In our model, a knowledgeaware subgraph pooling strategy was designed to capture the local and global environments around the ionization sites for micro-pK_(a) prediction. To overcome the scarcity of accurate pK_(a) data, lowfidelity data(computational pK_(a)) was used to fit the high-fidelity data(experimental pK_(a)) through transfer learning. The final MF-SuP-pK_(a) model was constructed by pre-training on the augmented ChEMBL data set and fine-tuning on the DataWarrior data set. Extensive evaluation on the DataWarrior data set and three benchmark data sets shows that MF-SuP-pK_(a) achieves superior performances to the state-of-theart pK_(a) prediction models while requires much less high-fidelity training data. Compared with Attentive FP, MF-SuP-pK_(a) achieves 23.83% and 20.12% improvement in terms of mean absolute error(MAE) on the acidic and basic sets, respectively. 展开更多
关键词 pK_(a)prediction Graph neural network subgraph pooling Multi-fidelity learning Data augmentation
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Suboptimal network coding subgraph algorithms for 5G minimum-cost multicast networks 被引量:1
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作者 Feng WEI Wei-xia ZOU 《Frontiers of Information Technology & Electronic Engineering》 SCIE EI CSCD 2018年第5期662-673,共12页
To reduce the transmission cost in 5G multicast networks that have separate control and data planes, we focus on the minimum-power-cost network-coding subgraph problem for the coexistence of two multieasts in wireless... To reduce the transmission cost in 5G multicast networks that have separate control and data planes, we focus on the minimum-power-cost network-coding subgraph problem for the coexistence of two multieasts in wireless networks. We propose two suboptimal algorithms as extensions of the Steiner tree multicast. The critical 1-cut path eliminating (C1CPE) algorithm attempts to find the minimum-cost solution for the coexistence of two multicast trees with the same throughput by reusing the links in the topology, and keeps the solution decodable by a coloring process. For the special case in which the two multicast trees share the same source and destinations, we propose the extended selective closest terminal first (E-SCTF) algorithm out of the CICPE algorithm. Theoretically the complexity of the E-SCTF algorithm is lower than that of the C1CPE algorithm. Simulation results show that both algorithms have superior performance in terms of power cost and that the advantage is more evident in networks with ultra-densification. 展开更多
关键词 Network coding subgraph Minimum power cost 5G Separation architecture
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High Performance Frequent Subgraph Mining on Transaction Datasets: A Survey and Performance Comparison 被引量:3
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作者 Bismita S.Jena Cynthia Khan Rajshekhar Sunderraman 《Big Data Mining and Analytics》 2019年第3期159-180,共22页
Graph data mining has been a crucial as well as inevitable area of research.Large amounts of graph data are produced in many areas,such as Bioinformatics,Cheminformatics,Social Networks,etc.Scalable graph data mining ... Graph data mining has been a crucial as well as inevitable area of research.Large amounts of graph data are produced in many areas,such as Bioinformatics,Cheminformatics,Social Networks,etc.Scalable graph data mining methods are getting increasingly popular and necessary due to increased graph complexities.Frequent subgraph mining is one such area where the task is to find overly recurring patterns/subgraphs.To tackle this problem,many main memory-based methods were proposed,which proved to be inefficient as the data size grew exponentially over time.In the past few years,several research groups have attempted to handle the Frequent Subgraph Mining(FSM)problem in multiple ways.Many authors have tried to achieve better performance using Graphic Processing Units(GPUs)which has multi-fold improvement over in-memory while dealing with large datasets.Later,Google’s MapReduce model with the Hadoop framework proved to be a major breakthrough in high performance large batch processing.Although MapReduce came with many benefits,its disk I/O and noniterative style model could not help much for FSM domain since subgraph mining process is an iterative approach.In recent years,Spark has emerged to be the De Facto industry standard with its distributed in-memory computing capability.This is a right fit solution for iterative style of programming as well.In this survey,we cover how high-performance computing has helped in improving the performance tremendously in the transactional directed and undirected aspect of graphs and performance comparisons of various FSM techniques are done based on experimental results. 展开更多
关键词 frequent subgraphS ISOMORPHISM SPARK
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The Hamilton-Connectivity with the Degree Sum of Non-adjacent Subgraphs of Claw-free Graphs
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作者 Wei ZHENG Li-gong WANG 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2019年第3期580-590,共11页
The degree d(H)of a subgraph H of a graph G is|u∈∪V(H)N(u)-V(H)|,where N(u)denotes the neighbor set of the vertex u of G.In this paper,we prove the following result on the condition of the degrees of subgraphs.Let G... The degree d(H)of a subgraph H of a graph G is|u∈∪V(H)N(u)-V(H)|,where N(u)denotes the neighbor set of the vertex u of G.In this paper,we prove the following result on the condition of the degrees of subgraphs.Let G be a 2-connected claw-free graph of order n with minimum degreeδ(G)≥3.If for any three non-adjacent subgraphs H1,H2,H3 that are isomorphic to K1,K1,K2,respectively,there is d(H1)+d(H2)+d(H3)≥n+3,then for each pair of vertices u,v∈G that is not a cut set,there exists a Hamilton path between u and v. 展开更多
关键词 CLAW-FREE graph non-adjacent subgraph degree of subgraph Hamilton path
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THE ASCENDING SUBGRAPH DECOMPOSITION OF K_n-H_(2n-1)
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作者 MA Kejie(Institute of Operations Research in Qufu Normal University, Qufu 273165, China)ZHANG Yuzhong(Institute of Applied Mathematics, Academia Sinica, Beijing 100080, China) 《Systems Science and Mathematical Sciences》 SCIE EI CSCD 1997年第4期356-360,共5页
A conjecture concerning a new kind of subgraph decomposition, the ascendingsubgraph decomposition, was proposed by Alavi Y. et al., as follows: Every graph ofpositive size has an ascending subgraph decomposition. In t... A conjecture concerning a new kind of subgraph decomposition, the ascendingsubgraph decomposition, was proposed by Alavi Y. et al., as follows: Every graph ofpositive size has an ascending subgraph decomposition. In this paper it is proved thatG = Kn- H2n-1 has an ascending subgraph decomposition, where H2n-1 is any graphwith at most n venices and at most 2n - 1 edges (n > 6). 展开更多
关键词 CONJECTURE ascending subgraph decomposition.
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Induced Subgraphs with Large Degrees at End-vertices for Hamiltonicity of Claw-free Graphs
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作者 Roman CADA Bin Long LI +1 位作者 Bo NING Sheng Gui ZHANG 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2016年第7期845-855,共11页
A graph is called claw-free if it contains no induced subgrapn lsomorpmc to K1,3. Matthews and Sumner proved that a 2-connected claw-free graph G is Hamiltonian if every vertex of it has degree at least ([V(G)I - 2... A graph is called claw-free if it contains no induced subgrapn lsomorpmc to K1,3. Matthews and Sumner proved that a 2-connected claw-free graph G is Hamiltonian if every vertex of it has degree at least ([V(G)I - 2)/3. At the workshop CSzC (Novy Smokovec, 1993), Broersma conjectured the degree condition of this result can be restricted only to end-vertices of induced copies of N (the graph obtained from a triangle by adding three disjoint pendant edges). Fujisawa and Yamashita showed that the degree condition of Matthews and Sumner can be restricted only to end-vertices of induced copies of Z1 (the graph obtained from a triangle by adding one pendant edge). Our main result in this paper is a characterization of all graphs H such that a 2-connected claw-free graph G is Hamiltonian if eachend-vertex of every induced copy of H in G has degree at least IV(G)I/3 + 1. This gives an affirmative solution of the conjecture of Broersma up to an additive constant.end-vertex of every induced copy of H in G has degree at least IV(G)I/3 + 1. This gives an affirmative solution of the conjecture of Broersma up to an additive constant. 展开更多
关键词 Induced subgraph large degree end-vertex claw-free graph Hamiltonian graph
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Four Forbidden Subgraph Pairs for Hamiltonicity of 3-connected Graphs
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作者 Hou-yuan LIN Zhi-quan HU 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2016年第2期469-476,共8页
For non-negative integers i,j and k, we denote the generalized net as Ni,j,k, which is a triangle with disjoint paths of length i, j and k, attached to distinct vertices of the triangle. In this paper, we prove that e... For non-negative integers i,j and k, we denote the generalized net as Ni,j,k, which is a triangle with disjoint paths of length i, j and k, attached to distinct vertices of the triangle. In this paper, we prove that every 3-connected {K1,3,N8-i,i,1}-free graph is hamiltonian, where 1〈i〈4. 展开更多
关键词 hamiltonian cycle forbidden subgraphs claw-free graphs CLOSURE
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