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4connected projectiveplanar graphs are Hamiltonian
 J. Combin. Theory Ser. B
, 1994
"... We prove the result stated in the title (conjectured by Grünbaum), and a conjecture of Plummer that every graph which can be obtained from a 4–connected planar graph by deleting two vertices is Hamiltonian. The proofs are constructive and give rise to polynomial–time algorithms. 2 1. ..."
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Cited by 27 (9 self)
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We prove the result stated in the title (conjectured by Grünbaum), and a conjecture of Plummer that every graph which can be obtained from a 4–connected planar graph by deleting two vertices is Hamiltonian. The proofs are constructive and give rise to polynomial–time algorithms. 2 1.
Hamiltonianconnected graphs
, 2008
"... For a simple graph G, let NC D(G) = min{N(u) ∪ N(v)  + d(w) : u, v, w ∈ V (G), uv ∈ E(G), wv or wu ∈ E(G)}. In this paper, we prove that if NC D(G) ≥ V (G), then either G is Hamiltonianconnected, or G belongs to a wellcharacterized class of graphs. The former results by Dirac, Ore and Fau ..."
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For a simple graph G, let NC D(G) = min{N(u) ∪ N(v)  + d(w) : u, v, w ∈ V (G), uv ∈ E(G), wv or wu ∈ E(G)}. In this paper, we prove that if NC D(G) ≥ V (G), then either G is Hamiltonianconnected, or G belongs to a wellcharacterized class of graphs. The former results by Dirac, Ore
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
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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as follows: ffl We devise a model for dynamic graph algorithms, based on performing queries and updates on an implicit representation of the drawing, and we show its applications. ffl We present several efficient dynamic drawing algorithms for trees, seriesparallel digraphs, planar stdigraphs, and planar
A fast and high quality multilevel scheme for partitioning irregular graphs
 SIAM JOURNAL ON SCIENTIFIC COMPUTING
, 1998
"... Recently, a number of researchers have investigated a class of graph partitioning algorithms that reduce the size of the graph by collapsing vertices and edges, partition the smaller graph, and then uncoarsen it to construct a partition for the original graph [Bui and Jones, Proc. ..."
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Cited by 1173 (16 self)
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Recently, a number of researchers have investigated a class of graph partitioning algorithms that reduce the size of the graph by collapsing vertices and edges, partition the smaller graph, and then uncoarsen it to construct a partition for the original graph [Bui and Jones, Proc.
An algebraic characterization of projectiveplanar graphs
, 2002
"... We give a detailed algebraic characterization of when a graph G can be imbedded in the projective plane. The characterization is in terms of the existence of a dual graph G ∗ on the same edge set as G which satisfies algebraic conditions inspired by homology groups and intersection products in homol ..."
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Cited by 2 (1 self)
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We give a detailed algebraic characterization of when a graph G can be imbedded in the projective plane. The characterization is in terms of the existence of a dual graph G ∗ on the same edge set as G which satisfies algebraic conditions inspired by homology groups and intersection products
A new proof that 4connected planar graphs are Hamiltonianconnected
, 2014
"... We proveatheorem guaranteeing specialpathsof faces in2connected planegraphs. As a corollary, we obtain a new proof of Thomassen’s theorem that every 4connected planar graph is Hamiltonianconnected. 1 ..."
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We proveatheorem guaranteeing specialpathsof faces in2connected planegraphs. As a corollary, we obtain a new proof of Thomassen’s theorem that every 4connected planar graph is Hamiltonianconnected. 1
Closure and HamiltonianConnectivity of ClawFree Graphs
 Discrete Math
, 1999
"... In [3], the closure cl(G) for a clawfree graph G is defined, and it is proved that G is hamiltonian if and only if cl(G) is hamiltonian. On the other hand, there exist infinitely many clawfree graphs G such that G is not hamiltonianconnected (resp. homogeneously traceable) while cl(G) is hamilton ..."
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Cited by 5 (3 self)
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In [3], the closure cl(G) for a clawfree graph G is defined, and it is proved that G is hamiltonian if and only if cl(G) is hamiltonian. On the other hand, there exist infinitely many clawfree graphs G such that G is not hamiltonianconnected (resp. homogeneously traceable) while cl
Interior Point Methods in Semidefinite Programming with Applications to Combinatorial Optimization
 SIAM Journal on Optimization
, 1993
"... We study the semidefinite programming problem (SDP), i.e the problem of optimization of a linear function of a symmetric matrix subject to linear equality constraints and the additional condition that the matrix be positive semidefinite. First we review the classical cone duality as specialized to S ..."
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Cited by 557 (12 self)
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to SDP. Next we present an interior point algorithm which converges to the optimal solution in polynomial time. The approach is a direct extension of Ye's projective method for linear programming. We also argue that most known interior point methods for linear programs can be transformed in a
Results 1  10
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79,667