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Efficient Enumeration of All Chordless Cycles in Graphs
"... Abstract. Enumerating chordless cycles is a theoretical important problem in the Graph Theory area. It also can be applied to practical problems, such as discover which predators compete for the same food in ecological networks. Motivated by theoretical interest of the problem and also by its sign ..."
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Abstract. Enumerating chordless cycles is a theoretical important problem in the Graph Theory area. It also can be applied to practical problems, such as discover which predators compete for the same food in ecological networks. Motivated by theoretical interest of the problem and also by its
DiracType Characterizations of Graphs Without Long Chordless Cycles
"... We call a chordless path v 1 v 2 : : : v i simplicial if it does not extend into any chordless path v 0 v 1 v 2 : : : v i v i+1 . Trivially, for every positive integer k, a graph contains no chordless cycle of length k + 3 or more if each of its nonempty induced subgraphs contains a simplicial path ..."
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Cited by 3 (0 self)
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We call a chordless path v 1 v 2 : : : v i simplicial if it does not extend into any chordless path v 0 v 1 v 2 : : : v i v i+1 . Trivially, for every positive integer k, a graph contains no chordless cycle of length k + 3 or more if each of its nonempty induced subgraphs contains a simplicial path
For Which Graphs Does Every Edge Belong to Exactly Two Chordless Cycles?
, 1996
"... Agraphis2cycled if each edge is contained in exactly two of its chordless cycles. The 2cycled graphs arise in connection with the study of balanced signing of graphs and matrices. The concept of balance of a {0, +1, 1} matrix or a signed bipartite graph has been studied by Truemper and by Con ..."
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Agraphis2cycled if each edge is contained in exactly two of its chordless cycles. The 2cycled graphs arise in connection with the study of balanced signing of graphs and matrices. The concept of balance of a {0, +1, 1} matrix or a signed bipartite graph has been studied by Truemper
Version 11.0 Fast Parallel Algorithm for Enumerating All Chordless Cycles in Graphs
"... Finding chordless cycles is an important theoretical problem in the Graph Theory area. It also can be applied to practical problems such as discover which predators compete for the same food in ecological networks. Motivated by the problem of theoretical interest and also by its significant practic ..."
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Finding chordless cycles is an important theoretical problem in the Graph Theory area. It also can be applied to practical problems such as discover which predators compete for the same food in ecological networks. Motivated by the problem of theoretical interest and also by its significant
On the generation of the chordless fourcycle
 Biometrika
, 2000
"... In the theory of Markov graphical representations of conditional independencies a special role is played by the chordless fourcycle, representing for four random variables the conditional independencies X ⊥ V  (U, W) and W ⊥ U  (X, V). It is not immediately clear how such systems are to be genera ..."
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Cited by 2 (0 self)
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In the theory of Markov graphical representations of conditional independencies a special role is played by the chordless fourcycle, representing for four random variables the conditional independencies X ⊥ V  (U, W) and W ⊥ U  (X, V). It is not immediately clear how such systems
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.
Chordless paths through three vertices
, 2006
"... Consider the following problem, which we call “Chordless path through three vertices ” or CP3V, for short: Given a simple undirected graph G = (V, E), a positive integer k, and three distinct vertices s, t, and v ∈ V, is there a chordless path of length at most k from s via v to t in G? In a chordle ..."
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Cited by 14 (0 self)
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complexity of CP3V by proving it W [1]complete with respect to its natural parameter k. Our reduction extends to a number of related problems about chordless paths and cycles. In particular, deciding on the existence of a single directed chordless (s, t)path in a digraph is also W [1]complete with respect
On parameterized path and chordless path problems
 In 22nd IEEE Conference on Computational Complexity
, 2007
"... All intext references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately. ..."
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Cited by 12 (5 self)
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All intext references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately.
Results 1  10
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