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An edge colouring of multigraphs
 COMPUTER SCIENCE JOURNAL OF MOLDOVA, VOL.15, NO.2(44)
, 2007
"... We consider a strict kcolouring of a multigraph G as a surjection f from the vertex set of G into a set of colours {1,2,...,k} such that, for every nonpendant vertex x of G, there exist at least two edges incident to x and coloured by the same colour. The maximum number of colours in a strict edge ..."
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We consider a strict kcolouring of a multigraph G as a surjection f from the vertex set of G into a set of colours {1,2,...,k} such that, for every nonpendant vertex x of G, there exist at least two edges incident to x and coloured by the same colour. The maximum number of colours in a strict
Partitions and Edge Colourings of Multigraphs
"... Erdős and Lovász conjectured in 1968 that for every graph G with χ(G)> ω(G) and any two integers s, t ≥ 2 with s + t = χ(G) + 1, there is a partition (S, T) of the vertex set V (G) such that χ(G[S]) ≥ s and χ(G[T]) ≥ t. Except for a few cases, this conjecture is still unsolved. In this note we ..."
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prove the conjecture for line graphs of multigraphs. 1
Alternating Cycles and Trails in 2EdgeColoured Complete Multigraphs
, 1998
"... We consider edgecoloured multigraphs. A trail in such a multigraph is alternating if its successive edges differ in colour. Let G be a 2edgecoloured complete graph and let M be a 2edgecoloured complete multigraph. M. Bankfalvi and Zs. Bankfalvi [2] obtained a necessary and sufficient condition ..."
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Cited by 3 (0 self)
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We consider edgecoloured multigraphs. A trail in such a multigraph is alternating if its successive edges differ in colour. Let G be a 2edgecoloured complete graph and let M be a 2edgecoloured complete multigraph. M. Bankfalvi and Zs. Bankfalvi [2] obtained a necessary and sufficient
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
Histograms of Oriented Gradients for Human Detection
 In CVPR
, 2005
"... We study the question of feature sets for robust visual object recognition, adopting linear SVM based human detection as a test case. After reviewing existing edge and gradient based descriptors, we show experimentally that grids of Histograms of Oriented Gradient (HOG) descriptors significantly out ..."
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Cited by 3678 (9 self)
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We study the question of feature sets for robust visual object recognition, adopting linear SVM based human detection as a test case. After reviewing existing edge and gradient based descriptors, we show experimentally that grids of Histograms of Oriented Gradient (HOG) descriptors significantly
Finding community structure in networks using the eigenvectors of matrices
, 2006
"... We consider the problem of detecting communities or modules in networks, groups of vertices with a higherthanaverage density of edges connecting them. Previous work indicates that a robust approach to this problem is the maximization of the benefit function known as “modularity ” over possible div ..."
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Cited by 500 (0 self)
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We consider the problem of detecting communities or modules in networks, groups of vertices with a higherthanaverage density of edges connecting them. Previous work indicates that a robust approach to this problem is the maximization of the benefit function known as “modularity ” over possible
A Critical Point For Random Graphs With A Given Degree Sequence
, 2000
"... Given a sequence of nonnegative real numbers 0 ; 1 ; : : : which sum to 1, we consider random graphs having approximately i n vertices of degree i. Essentially, we show that if P i(i \Gamma 2) i ? 0 then such graphs almost surely have a giant component, while if P i(i \Gamma 2) i ! 0 the ..."
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Cited by 511 (8 self)
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Given a sequence of nonnegative real numbers 0 ; 1 ; : : : which sum to 1, we consider random graphs having approximately i n vertices of degree i. Essentially, we show that if P i(i \Gamma 2) i ? 0 then such graphs almost surely have a giant component, while if P i(i \Gamma 2) i ! 0 then almost surely all components in such graphs are small. We can apply these results to G n;p ; G n;M , and other wellknown models of random graphs. There are also applications related to the chromatic number of sparse random graphs.
On the statistical analysis of dirty pictures
 JOURNAL OF THE ROYAL STATISTICAL SOCIETY B
, 1986
"... ..."
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