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Tutte sets in graphs II: The complexity of finding maximum Tutte sets
 Discrete Appl. Math
"... ∗Part of this research was done while the first two authors were visiting the Universita ́ di Roma. The hospitality and financial support are gratefully acknowledged. 1 A wellknown formula of Tutte and Berge expresses the size of a maximum matching in a graph G in terms of what is usually called th ..."
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Cited by 3 (2 self)
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of finding Tutte sets in a graph. We first give two polynomial algorithms for finding a maximal Tutte set. We then consider the complexity of finding a maximum Tutte set, and show it is NPhard for general graphs, as well as for several interesting restricted classes such as planar graphs. By contrast, we
A Tutte polynomial for signed graphs
 Discrete Appl. Math
, 1989
"... This paper introduces a generalization of the Tutte polynomial [14] that is defined for signed graphs. A signed graph is a graph whose edges are each labelled with a sign (+l or 1). The generalized polynomial will be denoted Q[G] = Q[G](A, B, d). Here G is the signed graph, and the letters A, B, d ..."
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Cited by 35 (2 self)
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This paper introduces a generalization of the Tutte polynomial [14] that is defined for signed graphs. A signed graph is a graph whose edges are each labelled with a sign (+l or 1). The generalized polynomial will be denoted Q[G] = Q[G](A, B, d). Here G is the signed graph, and the letters A, B
Computing Tutte Polynomials
 THE FIRST CENSUS ON THE TERTIARY INDUSTRY IN CHINA: SUMMARY STATISTICS, CHINA STATISTICAL
, 1996
"... The Tutte polynomial of a graph, also known as the partition function of the qstate Potts model, is a 2variable polynomial graph invariant of considerable importance in both combinatorics and statistical physics. It contains several other polynomial invariants, such as the chromatic polynomial an ..."
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Cited by 16 (1 self)
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The Tutte polynomial of a graph, also known as the partition function of the qstate Potts model, is a 2variable polynomial graph invariant of considerable importance in both combinatorics and statistical physics. It contains several other polynomial invariants, such as the chromatic polynomial
AN n 5/2 ALGORITHM FOR MAXIMUM MATCHINGS IN BIPARTITE GRAPHS
, 1973
"... The present paper shows how to construct a maximum matching in a bipartite graph with n vertices and m edges in a number of computation steps proportional to (m + n)x/. ..."
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Cited by 712 (1 self)
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The present paper shows how to construct a maximum matching in a bipartite graph with n vertices and m edges in a number of computation steps proportional to (m + n)x/.
The pyramid match kernel: Discriminative classification with sets of image features
 IN ICCV
, 2005
"... Discriminative learning is challenging when examples are sets of features, and the sets vary in cardinality and lack any sort of meaningful ordering. Kernelbased classification methods can learn complex decision boundaries, but a kernel over unordered set inputs must somehow solve for correspondenc ..."
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Cited by 546 (29 self)
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Discriminative learning is challenging when examples are sets of features, and the sets vary in cardinality and lack any sort of meaningful ordering. Kernelbased classification methods can learn complex decision boundaries, but a kernel over unordered set inputs must somehow solve
Community detection in graphs
, 2009
"... The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of th ..."
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Cited by 801 (1 self)
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The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices
Maximum entropy markov models for information extraction and segmentation
, 2000
"... Hidden Markov models (HMMs) are a powerful probabilistic tool for modeling sequential data, and have been applied with success to many textrelated tasks, such as partofspeech tagging, text segmentation and information extraction. In these cases, the observations are usually modeled as multinomial ..."
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Cited by 554 (18 self)
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, capitalization, formatting, partofspeech), and defines the conditional probability of state sequences given observation sequences. It does this by using the maximum entropy framework to fit a set of exponential models that represent the probability of a state given an observation and the previous state. We
A categorification for the Tutte polynomial
, 2006
"... For each graph, we construct a bigraded chain complex whose graded Euler characteristic is a version of the Tutte polynomial. This work is motivated by earlier work of Khovanov, HelmeGuizon and Rong, and others. ..."
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Cited by 3 (1 self)
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For each graph, we construct a bigraded chain complex whose graded Euler characteristic is a version of the Tutte polynomial. This work is motivated by earlier work of Khovanov, HelmeGuizon and Rong, and others.
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
Results 1  10
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