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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
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
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
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
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
A Note on TriangleFree and Bipartite Graphs
"... Using a clever inductive counting argument Erdos, Kleitman and Rothschild showed that almost all trianglefree graphs are bipartite, i.e., the cardinality of the two graph classes is asymptotically equal. In this paper we investigate the structure of the few trianglefree graphs which are not bipart ..."
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Cited by 1 (0 self)
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Using a clever inductive counting argument Erdos, Kleitman and Rothschild showed that almost all trianglefree graphs are bipartite, i.e., the cardinality of the two graph classes is asymptotically equal. In this paper we investigate the structure of the few trianglefree graphs which
Trianglefree subcubic graphs with minimum bipartite density
 J. Combin. Theory Ser. B
"... A graph is subcubic if its maximum degree is at most 3. The bipartite density of a graph G is max{ε(H)/ε(G) : H is a bipartite subgraph of G}, where ε(H) and ε(G) denote the numbers of edges in H and G, respectively. It is an NPhard problem to determine the bipartite density of any given trianglef ..."
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Cited by 7 (2 self)
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A graph is subcubic if its maximum degree is at most 3. The bipartite density of a graph G is max{ε(H)/ε(G) : H is a bipartite subgraph of G}, where ε(H) and ε(G) denote the numbers of edges in H and G, respectively. It is an NPhard problem to determine the bipartite density of any given trianglefree
Results 1  10
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80,159