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On the number of pentagons in trianglefree graphs
, 2011
"... Using the formalism of flag algebras, we prove that the maximal number of copies of C5 in a trianglefree graph with 5ℓ + a vertices (0 ≤ a ≤ 4) is ℓ 5−a (ℓ + 1) a, and we show that the set of extremal graphs for this problem consists precisely of almost balanced blowups of a single pentagon. This ..."
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Cited by 24 (5 self)
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Using the formalism of flag algebras, we prove that the maximal number of copies of C5 in a trianglefree graph with 5ℓ + a vertices (0 ≤ a ≤ 4) is ℓ 5−a (ℓ + 1) a, and we show that the set of extremal graphs for this problem consists precisely of almost balanced blowups of a single pentagon
Small Trianglefree . . . lines
, 2004
"... In the paper we show that all combinatorial trianglefree configurations for v ≤ 18 are geometrically realizable. We also show that there is a unique smallest astral (183) trianglefree configuration and its Levi graph is the generalized Petersen graph G(18, 5). In addition, we present geometric rea ..."
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In the paper we show that all combinatorial trianglefree configurations for v ≤ 18 are geometrically realizable. We also show that there is a unique smallest astral (183) trianglefree configuration and its Levi graph is the generalized Petersen graph G(18, 5). In addition, we present geometric
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
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
Independent Sets In TriangleFree Cubic Planar Graphs
"... We prove that every trianglefree planar graph on n vertices with maximum degree three has an independent set with size at least 3/8 n. This was suggested and later conjectured by Albertson, Bollobás, and Tucker. ..."
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Cited by 13 (1 self)
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We prove that every trianglefree planar graph on n vertices with maximum degree three has an independent set with size at least 3/8 n. This was suggested and later conjectured by Albertson, Bollobás, and Tucker.
Statistical mechanics of complex networks
 Rev. Mod. Phys
"... Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical links. While traditionally these systems were modeled as ra ..."
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Cited by 2083 (10 self)
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as random graphs, it is increasingly recognized that the topology and evolution of real
Dryad: Distributed DataParallel Programs from Sequential Building Blocks
 In EuroSys
, 2007
"... Dryad is a generalpurpose distributed execution engine for coarsegrain dataparallel applications. A Dryad application combines computational “vertices ” with communication “channels ” to form a dataflow graph. Dryad runs the application by executing the vertices of this graph on a set of availa ..."
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Cited by 730 (27 self)
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Dryad is a generalpurpose distributed execution engine for coarsegrain dataparallel applications. A Dryad application combines computational “vertices ” with communication “channels ” to form a dataflow graph. Dryad runs the application by executing the vertices of this graph on a set
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
The click modular router
, 2001
"... Click is a new software architecture for building flexible and configurable routers. A Click router is assembled from packet processing modules called elements. Individual elements implement simple router functions like packet classification, queueing, scheduling, and interfacing with network devic ..."
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Cited by 1155 (28 self)
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devices. A router configuration is a directed graph with elements at the vertices; packets flow along the edges of the graph. Configurations are written in a declarative language that supports userdefined abstractions. This language is both readable by humans and easily manipulated by tools. We present
Results 1  10
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109,385