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Colorful paths in vertex coloring of graphs
"... A colorful path in a graph G is a path with χ(G) vertices whose colors are different. A vcolorful path is such a path, starting from v. Let G 6 = C7 be a connected graph with maximum degree ∆(G). We show that there exists a (∆(G)+1)coloring of G with a vcolorful path for every v ∈ V (G). We also ..."
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Cited by 4 (0 self)
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A colorful path in a graph G is a path with χ(G) vertices whose colors are different. A vcolorful path is such a path, starting from v. Let G 6 = C7 be a connected graph with maximum degree ∆(G). We show that there exists a (∆(G)+1)coloring of G with a vcolorful path for every v ∈ V (G). 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
Pathrelated vertex colorings of graphs
"... We investigate algorithms for a frequency assignment problem in cellular networks. The problem can be modeled as a special coloring problem for graphs. Base stations are the vertices, ranges are the paths in the graph, and colors (frequencies) must be assigned to vertices following the conflictfree ..."
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We investigate algorithms for a frequency assignment problem in cellular networks. The problem can be modeled as a special coloring problem for graphs. Base stations are the vertices, ranges are the paths in the graph, and colors (frequencies) must be assigned to vertices following the conflict
Vertex distinguishing colorings of graphs with
 G) = 2, Discrete Mathematics 252(2002)17 ∼ 29
"... In a paper by Burris and Schelp [3], a conjecture was made concerning the number of colors χ′s(G) required to proper edgecolor G so that each vertex has a distinct set of colors incident to it. We consider the case when ∆(G) = 2, so that G is a union of paths and cycles. In particular we find the ..."
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Cited by 10 (2 self)
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In a paper by Burris and Schelp [3], a conjecture was made concerning the number of colors χ′s(G) required to proper edgecolor G so that each vertex has a distinct set of colors incident to it. We consider the case when ∆(G) = 2, so that G is a union of paths and cycles. In particular we find
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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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
Interprocedural Slicing Using Dependence Graphs
 ACM TRANSACTIONS ON PROGRAMMING LANGUAGES AND SYSTEMS
, 1990
"... ... This paper concerns the problem of interprocedural slicinggenerating a slice of an entire program, where the slice crosses the boundaries of procedure calls. To solve this problem, we introduce a new kind of graph to represent programs, called a system dependence graph, which extends previou ..."
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Cited by 822 (85 self)
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... This paper concerns the problem of interprocedural slicinggenerating a slice of an entire program, where the slice crosses the boundaries of procedure calls. To solve this problem, we introduce a new kind of graph to represent programs, called a system dependence graph, which extends
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
Efficiently computing static single assignment form and the control dependence graph
 ACM TRANSACTIONS ON PROGRAMMING LANGUAGES AND SYSTEMS
, 1991
"... In optimizing compilers, data structure choices directly influence the power and efficiency of practical program optimization. A poor choice of data structure can inhibit optimization or slow compilation to the point that advanced optimization features become undesirable. Recently, static single ass ..."
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Cited by 997 (8 self)
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assignment form and the control dependence graph have been proposed to represent data flow and control flow propertiee of programs. Each of these previously unrelated techniques lends efficiency and power to a useful class of program optimization. Although both of these structures are attractive
Graphs over Time: Densification Laws, Shrinking Diameters and Possible Explanations
, 2005
"... How do real graphs evolve over time? What are “normal” growth patterns in social, technological, and information networks? Many studies have discovered patterns in static graphs, identifying properties in a single snapshot of a large network, or in a very small number of snapshots; these include hea ..."
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Cited by 534 (48 self)
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How do real graphs evolve over time? What are “normal” growth patterns in social, technological, and information networks? Many studies have discovered patterns in static graphs, identifying properties in a single snapshot of a large network, or in a very small number of snapshots; these include
Results 1  10
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