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Drawings of Nonplanar Graphs with Crossingfree Subgraphs?
"... Abstract. We initiate the study of the following problem: Given a nonplanar graph G and a planar subgraph S of G, does there exist a straightline drawing Γ of G in the plane such that the edges of S are not crossed in Γ? We give positive and negative results for different kinds of spanning subgrap ..."
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Abstract. We initiate the study of the following problem: Given a nonplanar graph G and a planar subgraph S of G, does there exist a straightline drawing Γ of G in the plane such that the edges of S are not crossed in Γ? We give positive and negative results for different kinds of spanning
A Framework for Dynamic Graph Drawing
 CONGRESSUS NUMERANTIUM
, 1992
"... Drawing graphs is an important problem that combines flavors of computational geometry and graph theory. Applications can be found in a variety of areas including circuit layout, network management, software engineering, and graphics. The main contributions of this paper can be summarized as follows ..."
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Cited by 627 (44 self)
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as follows: ffl We devise a model for dynamic graph algorithms, based on performing queries and updates on an implicit representation of the drawing, and we show its applications. ffl We present several efficient dynamic drawing algorithms for trees, seriesparallel digraphs, planar stdigraphs, and planar
NonPlanar Extensions Of Planar Graphs
, 1999
"... A graph G is almost 4connected if it is simple, 3connected, has at least five vertices, and V (G) cannot be partitioned into three sets A; B; C in such a way that jCj = 3, jAj 2, jBj 2, and no edge of G has one end in A and the other end in B. A graph K is a subdivision of a graph G if K is ob ..."
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Cited by 3 (0 self)
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is obtained from G by replacing its edges by internally disjoint nonzero length paths with the same ends, called segments. Let G; H be almost 4connected graphs such that G is planar, H is nonplanar, and H has a subgraph isomorphic to a subdivision of G. If K is a subgraph of H, then a Kpath in H is a path
Confluent drawings: Visualizing NonPlanar Diagrams in a Planar Way
 GRAPH DRAWING (PROC. GD ’03), VOLUME 2912 OF LECTURE NOTES COMPUT. SCI
, 2003
"... We introduce a new approach for drawing diagrams. Our approach is to use a technique we call confluent drawing for visualizing nonplanar graphs in a planar way. This approach allows us to draw, in a crossingfree manner, graphs—such as software interaction diagrams—that would normally have many cro ..."
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Cited by 53 (9 self)
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We introduce a new approach for drawing diagrams. Our approach is to use a technique we call confluent drawing for visualizing nonplanar graphs in a planar way. This approach allows us to draw, in a crossingfree manner, graphs—such as software interaction diagrams—that would normally have many
Really straight drawings II: Nonplanar graphs
, 2005
"... We study straightline drawings of nonplanar graphs with few slopes. Interval graphs, cocomparability graphs and ATfree graphs are shown to have have drawings in which the number of slopes is bounded by the maximum degree. We prove that graphs of bounded degree and bounded treewidth have drawings ..."
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Cited by 1 (1 self)
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We study straightline drawings of nonplanar graphs with few slopes. Interval graphs, cocomparability graphs and ATfree graphs are shown to have have drawings in which the number of slopes is bounded by the maximum degree. We prove that graphs of bounded degree and bounded treewidth have
BendMinimal Orthogonal Drawing of NonPlanar Graphs
, 2004
"... This thesis belongs to the field of graph drawing research. It present s a new procedure for calculatp tl bend minimal shape of nonplanar graphswit givent opology. This met9 d is anextP,,9 oft he SimplePodevsnef drawing stKBRK9 SimplePodevsnef is a simplificatPD of t9 more complex Podevsnef  ..."
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Cited by 1 (1 self)
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of such bundles. The algorit9 present9 int hist hesis expandstd drawing st andard for nonplanar graphs. It tKpK crossing point of edges in a special way, and enablestbl t share identen9 grid points where appropriatK Hence it allows crossings of whole bundles of edges inst9 of single edges only. Furt,PB9EKp we
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
Factor Graphs and the SumProduct Algorithm
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 1998
"... A factor graph is a bipartite graph that expresses how a "global" function of many variables factors into a product of "local" functions. Factor graphs subsume many other graphical models including Bayesian networks, Markov random fields, and Tanner graphs. Following one simple c ..."
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Cited by 1787 (72 self)
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A factor graph is a bipartite graph that expresses how a "global" function of many variables factors into a product of "local" functions. Factor graphs subsume many other graphical models including Bayesian networks, Markov random fields, and Tanner graphs. Following one simple
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