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Planarizing Graphs  A Survey and Annotated Bibliography
, 1999
"... Given a finite, undirected, simple graph G, we are concerned with operations on G that transform it into a planar graph. We give a survey of results about such operations and related graph parameters. While there are many algorithmic results about planarization through edge deletion, the results abo ..."
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Cited by 32 (0 self)
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Given a finite, undirected, simple graph G, we are concerned with operations on G that transform it into a planar graph. We give a survey of results about such operations and related graph parameters. While there are many algorithmic results about planarization through edge deletion, the results
Drawing Planar Graphs with Large Vertices and Thick Edges
 Journal of Graph Algorithms and Applications
, 2004
"... We consider the problem of representing size information in the edges and vertices of a planar graph. Such information can be used, for example, to depict a network of computers and information traveling through the network. We present an efficient lineartime algorithm which draws edges and vertice ..."
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Cited by 10 (0 self)
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We consider the problem of representing size information in the edges and vertices of a planar graph. Such information can be used, for example, to depict a network of computers and information traveling through the network. We present an efficient lineartime algorithm which draws edges
EdgeOrienting on Split, Planar and Treelike Graphs
 Comput. J.
, 2007
"... Let G(V, E) be an undirected connected graph, where each vertex v is associated with a positive cost C(v) and each edge e 5 (u, v) is associated with two positive weights, W(u!v) and W(v!u). We consider a new graph problem, called the edgeorientation problem (the EOP). The major issue is to assign ..."
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each edge e 5 (u, v) an orientation, either from u to v, denoted as u!v, or from v to u, denoted as v!u, such that maxx[VfC(x) 1 Sx!z W(x!z)g is minimized. This paper first shows that the EOP is NPhard on split graphs and planar graphs. Then, a lineartime algorithm on star graphs is proposed
T.: The density of fanplanar graphs
 CoRR abs/1403.6184
"... A topological drawing of a graph is fanplanar if for each edge e the edges crossing e have a common endpoint on the same side of e, and a fanplanar graph is a graph admitting such a drawing. Equivalently, this can be formulated by two forbidden patterns, one of which is the configuration where e i ..."
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A topological drawing of a graph is fanplanar if for each edge e the edges crossing e have a common endpoint on the same side of e, and a fanplanar graph is a graph admitting such a drawing. Equivalently, this can be formulated by two forbidden patterns, one of which is the configuration where e
Contact Representations of NonPlanar Graphs
"... Abstract. We study contact representations of nonplanar graphs in which vertices are represented by axisaligned polyhedra in 3D and edges are realized by nonzero area common boundaries between corresponding polyhedra. We present a linertime algorithm constructing a representation of a 3connect ..."
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Abstract. We study contact representations of nonplanar graphs in which vertices are represented by axisaligned polyhedra in 3D and edges are realized by nonzero area common boundaries between corresponding polyhedra. We present a linertime algorithm constructing a representation of a 3
The Thickness of Graphs: A Survey
 Graphs Combin
, 1998
"... We give a stateoftheart survey of the thickness of a graph from both a theoretical and a practical point of view. After summarizing the relevant results concerning this topological invariant of a graph, we deal with practical computation of the thickness. We present some modifications of a ba ..."
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Cited by 22 (0 self)
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basic heuristic and investigate their usefulness for evaluating the thickness and determining a decomposition of a graph in planar subgraphs. Key words: Thickness, maximum planar subgraph, branch and cut 1 Introduction In VLSI circuit design, a chip is represented as a hypergraph consisting of nodes
On the thickness of graphs of given degree
 Inform. Sci
, 1991
"... The results presented here refer to the determination of the thickness of a graph; that is, the minimum number of planar subgraphs into which the graph can be decomposed. A useful general, preliminary result obtained is Theorem 8: that a planar graph always has a planar representation in which the n ..."
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Cited by 18 (0 self)
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The results presented here refer to the determination of the thickness of a graph; that is, the minimum number of planar subgraphs into which the graph can be decomposed. A useful general, preliminary result obtained is Theorem 8: that a planar graph always has a planar representation in which
Results 1  10
of
54,718