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342,526
A Separator Theorem for Planar Graphs
, 1977
"... Let G be any nvertex planar graph. We prove that the vertices of G can be partitioned into three sets A, B, C such that no edge joins a vertex in A with a vertex in B, neither A nor B contains more than 2n/3 vertices, and C contains no more than 2& & vertices. We exhibit an algorithm which ..."
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Cited by 465 (1 self)
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Let G be any nvertex planar graph. We prove that the vertices of G can be partitioned into three sets A, B, C such that no edge joins a vertex in A with a vertex in B, neither A nor B contains more than 2n/3 vertices, and C contains no more than 2& & vertices. We exhibit an algorithm which
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
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.
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 minimal trianglefree planar graphs with prescribed 1defective chromatic number
, 2012
"... ..."
TriangleFree Planar Graphs as Segment Intersection Graphs
 JOURNAL OF GRAPH ALGORITHMS AND APPLICATIONS
, 2002
"... We prove that every trianglefree planar graph is the intersection graph of a set of segments in the plane. Moreover, the segments can be chosen in only three directions (horizontal, vertical and oblique) and in such a way that no two segments cross, i.e., intersect in a common interior point. Th ..."
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Cited by 18 (0 self)
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We prove that every trianglefree planar graph is the intersection graph of a set of segments in the plane. Moreover, the segments can be chosen in only three directions (horizontal, vertical and oblique) and in such a way that no two segments cross, i.e., intersect in a common interior point
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
Results 1  10
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342,526