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Results 1 - 10
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93,196
A Separator Theorem for Planar Graphs
, 1977
"... Let G be any n-vertex planar graph. We prove that the vertices of G can be partitioned into three sets A, B, C such that no edge joins a vertex in A with a vertex in B, neither A nor B contains more than 2n/3 vertices, and C contains no more than 2& & vertices. We exhibit an algorithm which ..."
Abstract
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Cited by 465 (1 self)
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Let G be any n-vertex planar graph. We prove that the vertices of G can be partitioned into three sets A, B, C such that no edge joins a vertex in A with a vertex in B, neither A nor B contains more than 2n/3 vertices, and C contains no more than 2& & vertices. We exhibit an algorithm which
On Simultaneous Planar Graph Embeddings
- COMPUT. GEOM
, 2003
"... We consider the problem of simultaneous embedding of planar graphs. There are two variants ..."
Abstract
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Cited by 39 (10 self)
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We consider the problem of simultaneous embedding of planar graphs. There are two variants
Planar embedding of planar graphs
- Advances in Computing Research
, 1984
"... Planar embedding with minimal area of graphs on an integer grid is an interesting problem in VLSI theory. Valiant [12] gave an algorithm to construct a planar embedding for trees in linear area, he also proved that there are planar graphs that require quadratic area. We fill in a spectrum between Va ..."
Abstract
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Cited by 31 (1 self)
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Planar embedding with minimal area of graphs on an integer grid is an interesting problem in VLSI theory. Valiant [12] gave an algorithm to construct a planar embedding for trees in linear area, he also proved that there are planar graphs that require quadratic area. We fill in a spectrum between
Planar graphs as VPG-graphs
, 2013
"... A graph is Bk-VPG when it has an intersection representation by paths in a rectangular grid with at most k bends (turns). It is known that all planar graphs are B3-VPG and this was conjectured to be tight. We disprove this conjecture by showing that all planar graphs are B2-VPG. We also show that th ..."
Abstract
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Cited by 7 (3 self)
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A graph is Bk-VPG when it has an intersection representation by paths in a rectangular grid with at most k bends (turns). It is known that all planar graphs are B3-VPG and this was conjectured to be tight. We disprove this conjecture by showing that all planar graphs are B2-VPG. We also show
Random planar graphs
- JOURNAL OF COMBINATORIAL THEORY, SERIES B 93 (2005) 187 –205
, 2005
"... We study various properties of the random planar graph Rn, drawn uniformly at random from the class Pn of all simple planar graphs on n labelled vertices. In particular, we show that the probability that Rn is connected is bounded away from 0 and from 1. We also show for example that each positive i ..."
Abstract
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Cited by 67 (20 self)
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We study various properties of the random planar graph Rn, drawn uniformly at random from the class Pn of all simple planar graphs on n labelled vertices. In particular, we show that the probability that Rn is connected is bounded away from 0 and from 1. We also show for example that each positive
Matched Drawings of Planar Graphs
, 2007
"... A natural way to draw two planar graphs whose vertex sets are matched is to assign each matched pair a unique y-coordinate. In this paper we introduce the concept of such matched drawings, which are a relaxation of simultaneous geometric embeddings with mapping. We study which classes of graphs all ..."
Abstract
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Cited by 7 (3 self)
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A natural way to draw two planar graphs whose vertex sets are matched is to assign each matched pair a unique y-coordinate. In this paper we introduce the concept of such matched drawings, which are a relaxation of simultaneous geometric embeddings with mapping. We study which classes of graphs
On Random Planar Graphs, the Number of Planar Graphs and Their Triangulations
- Jombinatorial Theory, Series B
, 2001
"... Let Pn be the set of labelled planar graphs with n vertices. Denise, Vasconcellos and Welsh proved that jPn j n! 75:8 n+o(n) and Bender, Gao and Wormald proved that jPn j n! 26:1 n+o(n) . McDiarmid proved that almost all graphs in Pn have at least 13=7n edges. In this paper, we show that jPn j n! 37 ..."
Abstract
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Cited by 28 (1 self)
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Let Pn be the set of labelled planar graphs with n vertices. Denise, Vasconcellos and Welsh proved that jPn j n! 75:8 n+o(n) and Bender, Gao and Wormald proved that jPn j n! 26:1 n+o(n) . McDiarmid proved that almost all graphs in Pn have at least 13=7n edges. In this paper, we show that jPn j n
Supereulerian planar graphs
, 2003
"... We investigate the supereulerian graph problems within planar graphs, and we prove that if a 2-edge-connected planar graph G is at most three edges short of having two edge-disjoint spanning trees, then G is supereulerian except a few classes of graphs. This is applied to show the existence of spann ..."
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We investigate the supereulerian graph problems within planar graphs, and we prove that if a 2-edge-connected planar graph G is at most three edges short of having two edge-disjoint spanning trees, then G is supereulerian except a few classes of graphs. This is applied to show the existence
Simultaneous Embedding of Planar Graphs
, 2002
"... Given a planar graph G with n vertices, we provide an algorithm to find a straight-line planar embedding of G on an O(n⁴) × O(n⁴) grid, so that the vertices of G lie in general position. We then show how this algorithm can be used for obtaining a simultaneous embedding of two planar graphs when one ..."
Abstract
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Given a planar graph G with n vertices, we provide an algorithm to find a straight-line planar embedding of G on an O(n⁴) × O(n⁴) grid, so that the vertices of G lie in general position. We then show how this algorithm can be used for obtaining a simultaneous embedding of two planar graphs when
Results 1 - 10
of
93,196
