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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
On The Edge Distribution In TriangleFree Graphs
 J. Combin. Theory Ser. B
, 1995
"... Two problems on the edge distribution in trianglefree graphs are considered: 1) Given an 0 < < 1. Find the largest = () such that for innitely many n there exists a trianglefree graph G on n vertices in which every n vertices span at least n 2 edges. This problem was considered by Erd ..."
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Cited by 14 (0 self)
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Two problems on the edge distribution in trianglefree graphs are considered: 1) Given an 0 < < 1. Find the largest = () such that for innitely many n there exists a trianglefree graph G on n vertices in which every n vertices span at least n 2 edges. This problem was considered
On Generating TriangleFree Graphs
 PROC. AGT 2009
, 2009
"... We show that the problem to decide whether a graph can be made trianglefree with at most k edge deletions remains NPcomplete even when restricted to planar graphs of maximum degree seven. In addition, we provide polynomialtime data reduction rules for this problem and obtain problem kernels consi ..."
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Cited by 6 (0 self)
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We show that the problem to decide whether a graph can be made trianglefree with at most k edge deletions remains NPcomplete even when restricted to planar graphs of maximum degree seven. In addition, we provide polynomialtime data reduction rules for this problem and obtain problem kernels
On the Evolution of TriangleFree Graphs
, 1999
"... Denote by T (n; m) the class of all trianglefree graphs on n vertices and m edges. Our main result is the following sharp threshold, which answers the question for which densities a typical trianglefree graph is bipartite. Fix " > 0 and let t 3 = t 3 (n) = ( 3 16 n 3 log n) 1=2 . ..."
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Cited by 1 (1 self)
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Denote by T (n; m) the class of all trianglefree graphs on n vertices and m edges. Our main result is the following sharp threshold, which answers the question for which densities a typical trianglefree graph is bipartite. Fix " > 0 and let t 3 = t 3 (n) = ( 3 16 n 3 log n) 1
Median Graphs and TriangleFree Graphs
, 1997
"... Let M(m;n) be the complexity of checking whether a graph G with m ..."
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Cited by 31 (14 self)
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Let M(m;n) be the complexity of checking whether a graph G with m
Trianglefree subgraphs at the trianglefree process
, 903
"... We consider the trianglefree process: given an integer n, start by taking a uniformly random ordering of the edges of the complete nvertex graph Kn. Then, traverse the ordered edges and add each traversed edge to an (initially empty) evolving graph unless its addition creates a triangle. We study ..."
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Cited by 8 (0 self)
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We consider the trianglefree process: given an integer n, start by taking a uniformly random ordering of the edges of the complete nvertex graph Kn. Then, traverse the ordered edges and add each traversed edge to an (initially empty) evolving graph unless its addition creates a triangle. We
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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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
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
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