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762,309
Sharp Thresholds of Graph properties, and the ksat Problem
 J. Amer. Math. Soc
, 1998
"... Given a monotone graph property P , consider p (P ), the probability that a random graph with edge probability p will have P . The function d p (P )=dp is the key to understanding the threshold behavior of the property P . We show that if d p (P )=dp is small (corresponding to a nonsharp thres ..."
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Cited by 207 (7 self)
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Given a monotone graph property P , consider p (P ), the probability that a random graph with edge probability p will have P . The function d p (P )=dp is the key to understanding the threshold behavior of the property P . We show that if d p (P )=dp is small (corresponding to a non
Perfectness is an Elusive Graph Property
, 2003
"... A graph property is called elusive (or evasive) if every algorithm for testing this property has to read in the worst case Q) entries of the adjacency matrix of the given graph. Several graph properties have been shown to be elusive, e.g. planarity [2] or fccolorability [4]. A famous conjecture of ..."
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A graph property is called elusive (or evasive) if every algorithm for testing this property has to read in the worst case Q) entries of the adjacency matrix of the given graph. Several graph properties have been shown to be elusive, e.g. planarity [2] or fccolorability [4]. A famous conjecture
Algebraic Graph Theory
, 2011
"... Algebraic graph theory comprises both the study of algebraic objects arising in connection with graphs, for example, automorphism groups of graphs along with the use of algebraic tools to establish interesting properties of combinatorial objects. One of the oldest themes in the area is the investiga ..."
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Cited by 867 (12 self)
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Algebraic graph theory comprises both the study of algebraic objects arising in connection with graphs, for example, automorphism groups of graphs along with the use of algebraic tools to establish interesting properties of combinatorial objects. One of the oldest themes in the area
Perfectness is an Elusive Graph Property
, 2002
"... A graph property is called elusive (or evasive) if every algorithm for testing this property has to read in the worst case entries of the adjacency matrix of the given graph. Several graph properties have been shown to be elusive, e.g. planarity [3] or kcolorability [5]. A famous conjectur ..."
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Cited by 1 (0 self)
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A graph property is called elusive (or evasive) if every algorithm for testing this property has to read in the worst case entries of the adjacency matrix of the given graph. Several graph properties have been shown to be elusive, e.g. planarity [3] or kcolorability [5]. A famous
Introduction to testing graph properties
 In Property Testing
, 2010
"... Abstract. The aim of this article is to introduce the reader to the study of testing graph properties, while focusing on the main models and issues involved. No attempt is made to provide a comprehensive survey of this ..."
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Cited by 15 (1 self)
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Abstract. The aim of this article is to introduce the reader to the study of testing graph properties, while focusing on the main models and issues involved. No attempt is made to provide a comprehensive survey of this
GRAPH PROPERTIES OF GRAPH ASSOCIAHEDRA
"... Abstract. A graph associahedron is a simple polytope whose face lattice encodes the nested structure of the connected subgraphs of a given graph. In this paper, we study certain graph properties of the 1skeleta of graph associahedra, such as their diameter and their Hamiltonicity. Our results exte ..."
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Abstract. A graph associahedron is a simple polytope whose face lattice encodes the nested structure of the connected subgraphs of a given graph. In this paper, we study certain graph properties of the 1skeleta of graph associahedra, such as their diameter and their Hamiltonicity. Our results
Efficient GraphBased Image Segmentation
"... This paper addresses the problem of segmenting an image into regions. We define a predicate for measuring the evidence for a boundary between two regions using a graphbased representation of the image. We then develop an efficient segmentation algorithm based on this predicate, and show that althou ..."
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Cited by 930 (1 self)
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that although this algorithm makes greedy decisions it produces segmentations that satisfy global properties. We apply the algorithm to image segmentation using two different kinds of local neighborhoods in constructing the graph, and illustrate the results with both real and synthetic images. The algorithm
Graph properties based filtering
, 2006
"... Abstract. This article presents a generic filtering scheme, based on the graph description of global constraints. This description is defined by a network of binary constraints and a list of elementary graph properties: each solution of the global constraint corresponds to a subgraph of the initial ..."
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Cited by 3 (0 self)
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Abstract. This article presents a generic filtering scheme, based on the graph description of global constraints. This description is defined by a network of binary constraints and a list of elementary graph properties: each solution of the global constraint corresponds to a subgraph of the initial
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 475 (67 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
Functions and their basic properties
 JOURNAL OF FORMALIZED MATHEMATICS
, 2003
"... The definitions of the mode Function and the graph of a function are introduced. The graph of a function is defined to be identical with the function. The following concepts are also defined: the domain of a function, the range of a function, the identity function, the composition of functions, the ..."
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Cited by 1319 (31 self)
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The definitions of the mode Function and the graph of a function are introduced. The graph of a function is defined to be identical with the function. The following concepts are also defined: the domain of a function, the range of a function, the identity function, the composition of functions
Results 1  10
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762,309