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Edge Colouring Reduced Indifference Graphs
, 1999
"... The chromatic index problem  finding the minimum number of colours required for colouring the edges of a graph  is still unsolved for indifference graphs, whose vertices can be linearly ordered so that the vertices contained in the same maximal clique are consecutive in this order. Two adjacent ..."
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vertices are twins if they belong to the same maximal cliques. A graph is reduced if it contains no pair of twin vertices. We prove that every indifference graph having no twin maximum degree vertices is Class 1. We present two decomposition methods for edge colouring reduced indifference graphs. Key
On EdgeColouring Indifference Graphs
, 1997
"... . Vizing's theorem states that the chromatic index Ø 0 (G) of a graph G is either the maximum degree \Delta(G) or \Delta(G) + 1. A graph G is called overfull if jE(G)j ? \Delta(G)bjV (G)j=2c. A sufficient condition for Ø 0 (G) = \Delta(G) + 1 is that G contains an overfull subgraph H wit ..."
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Cited by 3 (3 self)
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and with no universal vertex, and for indifference graphs with odd maximum degree. For the latter subclass, we prove that Ø 0 = \Delta. 1 Introduction An edgecolouring of a graph is an assignment of colours to its edges such that no adjacent edges have the same colour. The chromatic index of a graph is the minimum
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
"GrabCut”  interactive foreground extraction using iterated graph cuts
 ACM TRANS. GRAPH
, 2004
"... The problem of efficient, interactive foreground/background segmentation in still images is of great practical importance in image editing. Classical image segmentation tools use either texture (colour) information, e.g. Magic Wand, or edge (contrast) information, e.g. Intelligent Scissors. Recently ..."
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Cited by 1140 (36 self)
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The problem of efficient, interactive foreground/background segmentation in still images is of great practical importance in image editing. Classical image segmentation tools use either texture (colour) information, e.g. Magic Wand, or edge (contrast) information, e.g. Intelligent Scissors
Graphbased algorithms for Boolean function manipulation
 IEEE TRANSACTIONS ON COMPUTERS
, 1986
"... In this paper we present a new data structure for representing Boolean functions and an associated set of manipulation algorithms. Functions are represented by directed, acyclic graphs in a manner similar to the representations introduced by Lee [1] and Akers [2], but with further restrictions on th ..."
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Cited by 3499 (47 self)
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In this paper we present a new data structure for representing Boolean functions and an associated set of manipulation algorithms. Functions are represented by directed, acyclic graphs in a manner similar to the representations introduced by Lee [1] and Akers [2], but with further restrictions
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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, and we observe some surprising phenomena. First, most of these graphs densify over time, with the number of edges growing superlinearly in the number of nodes. Second, the average distance between nodes often shrinks over time, in contrast to the conventional wisdom that such distance parameters should
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
On EdgeColouring Indifference Graphs
, 1994
"... Vizing's theorem states that the chromatic index Ø 0 (G) of a graph G is either the maximum degree \Delta(G) or \Delta(G) + 1. A graph G is called overfull if jE(G)j ? \Delta(G)bjV (G)j=2c. A sufficient condition for Ø 0 (G) = \Delta(G) +1 is that G contains an overfull subgraph H with \Del ..."
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vertex, and for indifference graphs with odd maximum degree. For the latter subclass, we prove that Ø 0 = \Delta. 1 Introduction An edgecolouring of a graph is an assignment of colours to its edges such that no adjacent edges have the same colour. The chromatic index of a Universidade Federal do
Goaldirected Requirements Acquisition
 SCIENCE OF COMPUTER PROGRAMMING
, 1993
"... Requirements analysis includes a preliminary acquisition step where a global model for the specification of the system and its environment is elaborated. This model, called requirements model, involves concepts that are currently not supported by existing formal specification languages, such as goal ..."
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Cited by 572 (17 self)
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, such as goals to be achieved, agents to be assigned, alternatives to be negotiated, etc. The paper presents an approach to requirements acquisition which is driven by such higherlevel concepts. Requirements models are acquired as instances of a conceptual metamodel. The latter can be represented as a graph
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