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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
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
The trianglefree process
 Adv. Math
, 2009
"... Consider the following stochastic graph process. We begin with G0, the empty graph on n vertices, and form Gi by adding a randomly chosen edge ei to Gi−1 where ei is chosen uniformly at random from the collection of pairs of vertices that neither appear as edges in Gi−1 nor form triangles when added ..."
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Cited by 33 (9 self)
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added as edges to Gi−1. Let the random variable M be the number of edges in the maximal triangle free graph generated by this process. We prove that asymptotically almost surely M = Θ(n 3/2 √ log n). This resolves a conjecture of Spencer. Furthermore, the independence number of GM is asymptotically
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
The Local Density of TriangleFree Graphs
, 1995
"... How dense can every induced subgraph of bffnc vertices (0 ! ff 1) of a trianglefree graph of order n be? Tools will be developed to estimate the local density of graphs, based on the spectrum of the graph and on a fractional viewpoint. These tools are used to refute a conjecture of Erdos et.al. ab ..."
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Cited by 5 (0 self)
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How dense can every induced subgraph of bffnc vertices (0 ! ff 1) of a trianglefree graph of order n be? Tools will be developed to estimate the local density of graphs, based on the spectrum of the graph and on a fractional viewpoint. These tools are used to refute a conjecture of Erdos et
TRIANGLEFREE TRIANGULATIONS
, 901
"... Abstract. The flip operation on colored innertrianglefree triangulations of a convex polygon is studied. It is shown that the affine Weyl group eCn acts transitively on these triangulations by colored flips, and that the resulting colored flip graph is closely related to a lower interval in the we ..."
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Cited by 1 (1 self)
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Abstract. The flip operation on colored innertrianglefree triangulations of a convex polygon is studied. It is shown that the affine Weyl group eCn acts transitively on these triangulations by colored flips, and that the resulting colored flip graph is closely related to a lower interval
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
Results 1  10
of
1,157,999