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A Sufficient Condition for The Existence of a Spanning Eulerian Subgraph in 2edgeConnected Graphs
, 1997
"... We prove that if G is a 2edgeconnected graph of order n 2: 14 and max{d{u),d(v)}> n3!) for each pair of nonadjacent vertices u ~ v of G. then G contains a spanning Eulerian subgraph and hence the line graph of G is Hamiltonian. ..."
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We prove that if G is a 2edgeconnected graph of order n 2: 14 and max{d{u),d(v)}> n3!) for each pair of nonadjacent vertices u ~ v of G. then G contains a spanning Eulerian subgraph and hence the line graph of G is Hamiltonian.
Spanning Eulerian Subgraphs in clawfree graphs
"... A graph is clawfree if it has no induced K1,3 subgraph. A graph is essential 4edgeconnected if removing at most three edges, the resulting graph has at most one component having edges. In this note, we show that every essential 4edgeconnected claw free graph has a spanning Eulerian subgraph with ..."
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Cited by 1 (1 self)
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A graph is clawfree if it has no induced K1,3 subgraph. A graph is essential 4edgeconnected if removing at most three edges, the resulting graph has at most one component having edges. In this note, we show that every essential 4edgeconnected claw free graph has a spanning Eulerian subgraph
gSpan: GraphBased Substructure Pattern Mining
, 2002
"... We investigate new approaches for frequent graphbased pattern mining in graph datasets and propose a novel algorithm called gSpan (graphbased Substructure pattern mining) , which discovers frequent substructures without candidate generation. gSpan builds a new lexicographic order among graphs, and ..."
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Cited by 639 (34 self)
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, and maps each graph to a unique minimum DFS code as its canonical label. Based on this lexicographic order, gSpan adopts the depthfirst search strategy to mine frequent connected subgraphs efficiently. Our performance study shows that gSpan substantially outperforms previous algorithms, sometimes
EULERIAN SUBGRAPHS in 3EdgeConnected Graps AND HAMILTONIAN LINE GRAPHS
, 2003
"... In this paper, we show that if G is a 3edgeconnected graph with S V ðGÞ and jSj 12, then either G has an Eulerian subgraph H such that S V ðHÞ,orG can be contracted to the Petersen graph in such a way that the preimage of each vertex of the Petersen graph contains at least one vertex in S. IfG is ..."
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Cited by 3 (2 self)
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In this paper, we show that if G is a 3edgeconnected graph with S V ðGÞ and jSj 12, then either G has an Eulerian subgraph H such that S V ðHÞ,orG can be contracted to the Petersen graph in such a way that the preimage of each vertex of the Petersen graph contains at least one vertex in S. If
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
Books in graphs
, 2008
"... A set of q triangles sharing a common edge is called a book of size q. We write β (n, m) for the the maximal q such that every graph G (n, m) contains a book of size q. In this note 1) we compute β ( n, cn 2) for infinitely many values of c with 1/4 < c < 1/3, 2) we show that if m ≥ (1/4 − α) ..."
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Cited by 2380 (22 self)
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A set of q triangles sharing a common edge is called a book of size q. We write β (n, m) for the the maximal q such that every graph G (n, m) contains a book of size q. In this note 1) we compute β ( n, cn 2) for infinitely many values of c with 1/4 < c < 1/3, 2) we show that if m ≥ (1/4 − α
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
The program dependence graph and its use in optimization
 ACM Transactions on Programming Languages and Systems
, 1987
"... In this paper we present an intermediate program representation, called the program dependence graph (PDG), that makes explicit both the data and control dependence5 for each operation in a program. Data dependences have been used to represent only the relevant data flow relationships of a program. ..."
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Cited by 989 (3 self)
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. Control dependence5 are introduced to analogously represent only the essential control flow relationships of a program. Control dependences are derived from the usual control flow graph. Many traditional optimizations operate more efficiently on the PDG. Since dependences in the PDG connect
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