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4,088
A Separator Theorem for Planar Graphs
, 1977
"... Let G be any nvertex 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 ..."
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Cited by 461 (1 self)
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Let G be any nvertex 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 ..."
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Cited by 42 (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 ..."
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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 VPGgraphs
, 2013
"... A graph is BkVPG 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 B3VPG and this was conjectured to be tight. We disprove this conjecture by showing that all planar graphs are B2VPG. We also show that th ..."
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Cited by 5 (3 self)
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A graph is BkVPG 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 B3VPG and this was conjectured to be tight. We disprove this conjecture by showing that all planar graphs are B2VPG. 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 ..."
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Cited by 66 (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
Acyclic colorings of planar graphs
 DISCRETE MATH
, 1991
"... It is shown that a planar graph can be partitioned into three linear forests. The sharpness of the result is also considered. ..."
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Cited by 9 (2 self)
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It is shown that a planar graph can be partitioned into three linear forests. The sharpness of the result is also considered.
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 ..."
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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
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 ycoordinate. 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 ..."
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Cited by 7 (2 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 ycoordinate. 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
Supereulerian planar graphs
, 2003
"... We investigate the supereulerian graph problems within planar graphs, and we prove that if a 2edgeconnected planar graph G is at most three edges short of having two edgedisjoint 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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Cited by 1 (1 self)
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We investigate the supereulerian graph problems within planar graphs, and we prove that if a 2edgeconnected planar graph G is at most three edges short of having two edgedisjoint spanning trees, then G is supereulerian except a few classes of graphs. This is applied to show the existence
The Random Planar Graph
 Congressus Numerantium
, 1996
"... We construct a Markov chain whose stationary distribution is uniform over all planar subgraphs of a graph. In the case of the complete graph our experiments suggest that the random simple planar graph on n vertices is connected but not 2connected and has approximately 2n edges. We present a rs ..."
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Cited by 38 (1 self)
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We construct a Markov chain whose stationary distribution is uniform over all planar subgraphs of a graph. In the case of the complete graph our experiments suggest that the random simple planar graph on n vertices is connected but not 2connected and has approximately 2n edges. We present a
Results 1  10
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4,088