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The independent domination number of maximal trianglefree graphs
, 2008
"... A trianglefree graph is maximal if the addition of any edge produces a triangle. A set S of vertices in a graph G is called an independent dominating set if S is both an independent and a dominating set of G. The independent domination number i(G) of G is the minimum cardinality of an independent d ..."
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Cited by 1 (0 self)
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A trianglefree graph is maximal if the addition of any edge produces a triangle. A set S of vertices in a graph G is called an independent dominating set if S is both an independent and a dominating set of G. The independent domination number i(G) of G is the minimum cardinality of an independent
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 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
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 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
The program dependence graph and its use in optimization
 ACM Transactions on Programming Languages and Systems
, 1987
"... In this paper we present an intermediate program representation, called the program dependence graph (PDG), that makes explicit both the data and control dependence5 for each operation in a program. Data dependences have been used to represent only the relevant data flow relationships of a program. ..."
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Cited by 989 (3 self)
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In this paper we present an intermediate program representation, called the program dependence graph (PDG), that makes explicit both the data and control dependence5 for each operation in a program. Data dependences have been used to represent only the relevant data flow relationships of a program
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.
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1,869,754