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850,602
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 214 (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
Books in graphs
, 2008
"... A set of q triangles sharing a common edge is called a book of size q. We write β (n, m) for the the maximal q such that every graph G (n, m) contains a book of size q. In this note 1) we compute β ( n, cn 2) for infinitely many values of c with 1/4 < c < 1/3, 2) we show that if m ≥ (1/4 − α) ..."
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Cited by 2380 (22 self)
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A set of q triangles sharing a common edge is called a book of size q. We write β (n, m) for the the maximal q such that every graph G (n, m) contains a book of size q. In this note 1) we compute β ( n, cn 2) for infinitely many values of c with 1/4 < c < 1/3, 2) we show that if m ≥ (1/4 − α
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
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
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
"... 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 868 (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
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
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
Results 1  10
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850,602