Two new hereditary classes of P 5-free graphs where the stability number can be found in polynomial time are proposed.They generalize several known results.
In this paper, we prove that every graph with maximum degree six that can be embedded in a surface of nonnegative characteristic is of Class I if it does not contain a 5- or 6-cycle with a chord, which extends some kn...In this paper, we prove that every graph with maximum degree six that can be embedded in a surface of nonnegative characteristic is of Class I if it does not contain a 5- or 6-cycle with a chord, which extends some known results.展开更多
Based on the framework of support vector machines （SVM） using one-against-one （OAO） strategy, a new multi-class kernel method based on directed aeyclie graph （DAG） and probabilistic distance is proposed to raise...Based on the framework of support vector machines （SVM） using one-against-one （OAO） strategy, a new multi-class kernel method based on directed aeyclie graph （DAG） and probabilistic distance is proposed to raise the multi-class classification accuracies. The topology structure of DAG is constructed by rearranging the nodes＇ sequence in the graph. DAG is equivalent to guided operating SVM on a list, and the classification performance depends on the nodes＇ sequence in the graph. Jeffries-Matusita distance （JMD） is introduced to estimate the separability of each class, and the implementation list is initialized with all classes organized according to certain sequence in the list. To testify the effectiveness of the proposed method, numerical analysis is conducted on UCI data and hyperspectral data. Meanwhile, comparative studies using standard OAO and DAG classification methods are also conducted and the results illustrate better performance and higher accuracy of the orooosed JMD-DAG method.展开更多
We investigate the dominating-c-color number,, of a graph G. That is the maximum number of color classes that are also dominating when G is colored using colors. We show that where is the join of G and . This result a...We investigate the dominating-c-color number,, of a graph G. That is the maximum number of color classes that are also dominating when G is colored using colors. We show that where is the join of G and . This result allows us to construct classes of graphs such that and thus provide some information regarding two questions raised in [1] and [2].展开更多
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 relations...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.展开更多
Learning Bayesian network structure is one of the most important branches in Bayesian network. The most popular graphical representative of a Bayesian network structure is an essential graph. This paper shows a combin...Learning Bayesian network structure is one of the most important branches in Bayesian network. The most popular graphical representative of a Bayesian network structure is an essential graph. This paper shows a combined algorithm according to the three rules for finding the essential graph of a given directed acyclic graph. Moreover, the complexity and advantages of this combined algorithm over others are also discussed. The aim of this paper is to present the proof of the correctness of the combined algorithm.展开更多
In this paper we present some results connected with still open problem of Gauss, negative Pell’s equation and some type graphs.In particular we prove in the Theorem 1 that all real quadratic fields K=Q( ) , generate...In this paper we present some results connected with still open problem of Gauss, negative Pell’s equation and some type graphs.In particular we prove in the Theorem 1 that all real quadratic fields K=Q( ) , generated by Fermat’s numbers with d=Fm+1=22m+1+1,m≥2, have not unique factorization. Theorem 2 give a connection of the Gauss problem with primitive Pythagorean triples. Moreover, in final part of our paper we indicate on some connections of the Gauss problem with odd graphs investigated by Cremona and Odoni in the papper [5].展开更多
Given a fixed prime number p, the multiplet of abelian type invariants of the p-class groups of all unramified cyclic degree p extensions of a number field K is called its IPAD (index-p abeliani- zation data). These i...Given a fixed prime number p, the multiplet of abelian type invariants of the p-class groups of all unramified cyclic degree p extensions of a number field K is called its IPAD (index-p abeliani- zation data). These invariants have proved to be a valuable information for determining the Galois group of the second Hilbert p-class field and the p-capitulation type of K. For p=3 and a number field K with elementary p-class group of rank two, all possible IPADs are given in the complete form of several infinite sequences. Iterated IPADs of second order are used to identify the group of the maximal unramified pro-p extension of K.展开更多
Let p be a prime and K be a number field with non-trivial p-class group ClpK. A crucial step in identifying the Galois group G∞p of the maximal unramified pro-p extension of K is to determine its two-stage approximat...Let p be a prime and K be a number field with non-trivial p-class group ClpK. A crucial step in identifying the Galois group G∞p of the maximal unramified pro-p extension of K is to determine its two-stage approximation M=G2pk, that is the second derived quotient M≃G/Gn. The family τ1K of abelian type invariants of the p-class groups ClpL of all unramified cyclic extensions L/K of degree p is called the index- abelianization data (IPAD) of K. It is able to specify a finite batch of contestants for the second p-class group M of K. In this paper we introduce two different kinds of generalized IPADs for obtaining more sophisticated results. The multi-layered IPAD (τ1Kτ(2)K) includes data on unramified abelian extensions L/K of degree p2 and enables sharper bounds for the order of M in the case Clpk≃(p,p,p), where current im-plementations of the p-group generation algorithm fail to produce explicit contestants for M , due to memory limitations. The iterated IPAD of second order τ(2)K contains information on non-abelian unramified extensions L/K of degree p2, or even p3, and admits the identification of the p-class tower group G for various infinite series of quadratic fields K=Q(√d) with ClpK≃(p,p) possessing a p-class field tower of exact length lpK=3 as a striking novelty.展开更多
基金The first author was supported by DIMACS Summer2 0 0 3Award
文摘Two new hereditary classes of P 5-free graphs where the stability number can be found in polynomial time are proposed.They generalize several known results.
基金Supported partially by the National Natural Science Foundation of China(11071223)the Zhejiang Natural Science Foundation of China(Z6090150)the Foundation of Zhejiang Educational Committee(Y201226078)
文摘In this paper, we prove that every graph with maximum degree six that can be embedded in a surface of nonnegative characteristic is of Class I if it does not contain a 5- or 6-cycle with a chord, which extends some known results.
基金Sponsored by the National Natural Science Foundation of China(Grant No.61201310)the Fundamental Research Funds for the Central Universities(Grant No.HIT.NSRIF.201160)the China Postdoctoral Science Foundation(Grant No.20110491067)
文摘Based on the framework of support vector machines （SVM） using one-against-one （OAO） strategy, a new multi-class kernel method based on directed aeyclie graph （DAG） and probabilistic distance is proposed to raise the multi-class classification accuracies. The topology structure of DAG is constructed by rearranging the nodes＇ sequence in the graph. DAG is equivalent to guided operating SVM on a list, and the classification performance depends on the nodes＇ sequence in the graph. Jeffries-Matusita distance （JMD） is introduced to estimate the separability of each class, and the implementation list is initialized with all classes organized according to certain sequence in the list. To testify the effectiveness of the proposed method, numerical analysis is conducted on UCI data and hyperspectral data. Meanwhile, comparative studies using standard OAO and DAG classification methods are also conducted and the results illustrate better performance and higher accuracy of the orooosed JMD-DAG method.
文摘We investigate the dominating-c-color number,, of a graph G. That is the maximum number of color classes that are also dominating when G is colored using colors. We show that where is the join of G and . This result allows us to construct classes of graphs such that and thus provide some information regarding two questions raised in [1] and [2].
基金Natural Science Foundation of Shandong Province of China (Y2004A04)Natural Science Foundation of Shandong Province of China (Y2006A12)Foundation of Ministry of Fujian Province Education of China (JA04268).
文摘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.
基金Supported by the National Natural Science Foundation of China (No. 60974082)
文摘Learning Bayesian network structure is one of the most important branches in Bayesian network. The most popular graphical representative of a Bayesian network structure is an essential graph. This paper shows a combined algorithm according to the three rules for finding the essential graph of a given directed acyclic graph. Moreover, the complexity and advantages of this combined algorithm over others are also discussed. The aim of this paper is to present the proof of the correctness of the combined algorithm.
文摘In this paper we present some results connected with still open problem of Gauss, negative Pell’s equation and some type graphs.In particular we prove in the Theorem 1 that all real quadratic fields K=Q( ) , generated by Fermat’s numbers with d=Fm+1=22m+1+1,m≥2, have not unique factorization. Theorem 2 give a connection of the Gauss problem with primitive Pythagorean triples. Moreover, in final part of our paper we indicate on some connections of the Gauss problem with odd graphs investigated by Cremona and Odoni in the papper [5].
文摘Given a fixed prime number p, the multiplet of abelian type invariants of the p-class groups of all unramified cyclic degree p extensions of a number field K is called its IPAD (index-p abeliani- zation data). These invariants have proved to be a valuable information for determining the Galois group of the second Hilbert p-class field and the p-capitulation type of K. For p=3 and a number field K with elementary p-class group of rank two, all possible IPADs are given in the complete form of several infinite sequences. Iterated IPADs of second order are used to identify the group of the maximal unramified pro-p extension of K.
文摘Let p be a prime and K be a number field with non-trivial p-class group ClpK. A crucial step in identifying the Galois group G∞p of the maximal unramified pro-p extension of K is to determine its two-stage approximation M=G2pk, that is the second derived quotient M≃G/Gn. The family τ1K of abelian type invariants of the p-class groups ClpL of all unramified cyclic extensions L/K of degree p is called the index- abelianization data (IPAD) of K. It is able to specify a finite batch of contestants for the second p-class group M of K. In this paper we introduce two different kinds of generalized IPADs for obtaining more sophisticated results. The multi-layered IPAD (τ1Kτ(2)K) includes data on unramified abelian extensions L/K of degree p2 and enables sharper bounds for the order of M in the case Clpk≃(p,p,p), where current im-plementations of the p-group generation algorithm fail to produce explicit contestants for M , due to memory limitations. The iterated IPAD of second order τ(2)K contains information on non-abelian unramified extensions L/K of degree p2, or even p3, and admits the identification of the p-class tower group G for various infinite series of quadratic fields K=Q(√d) with ClpK≃(p,p) possessing a p-class field tower of exact length lpK=3 as a striking novelty.
