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21,782
Line Graphs and Forbidden Induced Subgraphs
, 2001
"... Beineke and Robertson independently characterized line graphs in terms of nine forbidden induced subgraphs. In 1994, S8 oltes gave another characterization, which reduces the number of forbidden induced subgraphs to seven, with only five exceptional cases. A graph is said to be a dumbbell if it cons ..."
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Cited by 4 (1 self)
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Beineke and Robertson independently characterized line graphs in terms of nine forbidden induced subgraphs. In 1994, S8 oltes gave another characterization, which reduces the number of forbidden induced subgraphs to seven, with only five exceptional cases. A graph is said to be a dumbbell
Forbidden Subgraphs, Stability and Hamiltonicity
, 1998
"... We study the stability of some classes of clawfree graphs defined in terms of forbidden subgraphs under the closure operation defined in [10]. We characterize all connected graphs A such that the class of all CAfree graphs (where C denotes the claw) is stable. Using this result, we prove that ever ..."
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Cited by 7 (3 self)
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We study the stability of some classes of clawfree graphs defined in terms of forbidden subgraphs under the closure operation defined in [10]. We characterize all connected graphs A such that the class of all CAfree graphs (where C denotes the claw) is stable. Using this result, we prove
Property Testing and its connection to Learning and Approximation
"... We study the question of determining whether an unknown function has a particular property or is fflfar from any function with that property. A property testing algorithm is given a sample of the value of the function on instances drawn according to some distribution, and possibly may query the fun ..."
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Cited by 498 (68 self)
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the function on instances of its choice. First, we establish some connections between property testing and problems in learning theory. Next, we focus on testing graph properties, and devise algorithms to test whether a graph has properties such as being kcolorable or having a aeclique (clique of density ae
Forbidden subgraphs and the . . .
, 2013
"... The matching number of a graph is the maximum size of a set of vertexdisjoint edges. The transversal number is the minimum number of vertices needed to meet every edge. A graph has the KönigEgerváry property if its matching number equals its transversal number. Lovász proved a characterization of g ..."
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of graphs having the KönigEgerváry property by means of forbidden subgraphs within graphs with a perfect matching. Korach, Nguyen, and Peis proposed an extension of Lovász’s result to a characterization of all graphs having the KönigEgerváry property in terms of forbidden configurations (which are certain
Finding community structure in networks using the eigenvectors of matrices
, 2006
"... We consider the problem of detecting communities or modules in networks, groups of vertices with a higherthanaverage density of edges connecting them. Previous work indicates that a robust approach to this problem is the maximization of the benefit function known as “modularity ” over possible div ..."
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Cited by 500 (0 self)
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divisions of a network. Here we show that this maximization process can be written in terms of the eigenspectrum of a matrix we call the modularity matrix, which plays a role in community detection similar to that played by the graph Laplacian in graph partitioning calculations. This result leads us to a
Disjoint Stars and Forbidden Subgraphs
"... Let r, k be integers with r ≥ 3,k ≥ 2. We prove that if G is a K1,rfree graph of order at least (k − 1)(2r − 1) + 1 with δ(G) ≥ 2, then G contains k vertexdisjoint copies of K1,2. This result is motivated by characterizing a forbidden subgraph H which satisfies the statement “every Hfree graph o ..."
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Let r, k be integers with r ≥ 3,k ≥ 2. We prove that if G is a K1,rfree graph of order at least (k − 1)(2r − 1) + 1 with δ(G) ≥ 2, then G contains k vertexdisjoint copies of K1,2. This result is motivated by characterizing a forbidden subgraph H which satisfies the statement “every Hfree graph
Parameterized Complexity
, 1998
"... the rapidly developing systematic connections between FPT and useful heuristic algorithms  a new and exciting bridge between the theory of computing and computing in practice. The organizers of the seminar strongly believe that knowledge of parameterized complexity techniques and results belongs ..."
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Cited by 1218 (75 self)
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the rapidly developing systematic connections between FPT and useful heuristic algorithms  a new and exciting bridge between the theory of computing and computing in practice. The organizers of the seminar strongly believe that knowledge of parameterized complexity techniques and results belongs into the toolkit of every algorithm designer. The purpose of the seminar was to bring together leading experts from all over the world, and from the diverse areas of computer science that have been attracted to this new framework. The seminar was intended as the rst larger international meeting with a specic focus on parameterized complexity, and it hopefully serves as a driving force in the development of the eld. 1 We had 49 participants from Australia, Canada, India, Israel, New Zealand, USA, and various European countries. During the workshop 25 lectures were given. Moreover, one night session was devoted to open problems and Thursday was basically used for problem discussion
Graphical models, exponential families, and variational inference
, 2008
"... The formalism of probabilistic graphical models provides a unifying framework for capturing complex dependencies among random variables, and building largescale multivariate statistical models. Graphical models have become a focus of research in many statistical, computational and mathematical fiel ..."
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Cited by 800 (26 self)
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The formalism of probabilistic graphical models provides a unifying framework for capturing complex dependencies among random variables, and building largescale multivariate statistical models. Graphical models have become a focus of research in many statistical, computational and mathematical fields, including bioinformatics, communication theory, statistical physics, combinatorial optimization, signal and image processing, information retrieval and statistical machine learning. Many problems that arise in specific instances — including the key problems of computing marginals and modes of probability distributions — are best studied in the general setting. Working with exponential family representations, and exploiting the conjugate duality between the cumulant function and the entropy for exponential families, we develop general variational representations of the problems of computing likelihoods, marginal probabilities and most probable configurations. We describe how a wide varietyof algorithms — among them sumproduct, cluster variational methods, expectationpropagation, mean field methods, maxproduct and linear programming relaxation, as well as conic programming relaxations — can all be understood in terms of exact or approximate forms of these variational representations. The variational approach provides a complementary alternative to Markov chain Monte Carlo as a general source of approximation methods for inference in largescale statistical models.
The StructureMapping Engine: Algorithm and Examples
 Artificial Intelligence
, 1989
"... This paper describes the StructureMapping Engine (SME), a program for studying analogical processing. SME has been built to explore Gentner's Structuremapping theory of analogy, and provides a "tool kit" for constructing matching algorithms consistent with this theory. Its flexibili ..."
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Cited by 512 (115 self)
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This paper describes the StructureMapping Engine (SME), a program for studying analogical processing. SME has been built to explore Gentner's Structuremapping theory of analogy, and provides a "tool kit" for constructing matching algorithms consistent with this theory. Its flexibility enhances cognitive simulation studies by simplifying experimentation. Furthermore, SME is very efficient, making it a useful component in machine learning systems as well. We review the Structuremapping theory and describe the design of the engine. We analyze the complexity of the algorithm, and demonstrate that most of the steps are polynomial, typically bounded by O (N 2 ). Next we demonstrate some examples of its operation taken from our cognitive simulation studies and work in machine learning. Finally, we compare SME to other analogy programs and discuss several areas for future work. This paper appeared in Artificial Intelligence, 41, 1989, pp 163. For more information, please contact forbu...
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