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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
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
The 3edgecolouring problem on the
, 2009
"... We consider the problem of counting the number of 3colourings of the edges (bonds) of the 48 lattice and the 312 lattice. These lattices are Archimedean with coordination number 3, and can be regarded as decorated versions of the square and honeycomb lattice, respectively. We solve these edgecol ..."
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We consider the problem of counting the number of 3colourings of the edges (bonds) of the 48 lattice and the 312 lattice. These lattices are Archimedean with coordination number 3, and can be regarded as decorated versions of the square and honeycomb lattice, respectively. We solve these edgecolouring
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
Algebraic Graph Theory
"... Algebraic graph theory comprises both the study of algebraic objects arising in connection with graphs, for example, automorphism groups of graphs along with the use of algebraic tools to establish interesting properties of combinatorial objects. One of the oldest themes in the area is the investiga ..."
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Cited by 868 (12 self)
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regular fashion. These arise regularly in connection with extremal structures: such structures often have an unexpected degree of regularity and, because of this, often give rise to an association scheme. This in turn leads to a semisimple commutative algebra and the representation theory of this algebra
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
Coloured matchings in edgecoloured graphs
, 2007
"... Erdős � and Gallai proved that every graph of order n with more than f(k,n) = �2k−1� �k−1 � � max 2, 2 + (k − 1)(n − k + 1) edges contains a matching with k edges. We generalize this and show that if R (red) and B (blue) are graphs on the same vertex set of size n, each with more than f(k,n) edges, ..."
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, then the edgecoloured multigraph R ∪ B contains any 2edgecoloured matching with k edges. In general, we prove that for n ≥ 3k − 1, if G1,G2,...,Gt are graphs on the same vertex set of size n, such that the edges of Gi are coloured i and Gi has more than f(k,n) edges for all 1 ≤ i ≤ t, then the edgecoloured
Results 1  10
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1,447,871