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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
SEFE with No Mapping via Large Induced Outerplane Graphs in Plane Graphs
, 2013
"... We show that every nvertex planar graph admits a simultaneous embedding with no mapping and with fixed edges with any (n/2)vertex planar graph. In order to achieve this result, we prove that every nvertex plane graph has an induced outerplane subgraph containing at least n/2 vertices. Also, we ..."
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We show that every nvertex planar graph admits a simultaneous embedding with no mapping and with fixed edges with any (n/2)vertex planar graph. In order to achieve this result, we prove that every nvertex plane graph has an induced outerplane subgraph containing at least n/2 vertices. Also, we
Universal point sets for planar graph drawings with circular arcs
, 2013
"... Abstract We prove that there exists a set S of n points in the plane such that every nvertex planar graph G admits a planar drawing in which every vertex of G is placed on a distinct point of S and every edge of G is drawn as a circular arc. ..."
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Cited by 2 (0 self)
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Abstract We prove that there exists a set S of n points in the plane such that every nvertex planar graph G admits a planar drawing in which every vertex of G is placed on a distinct point of S and every edge of G is drawn as a circular arc.
COMPUTING THE GIRTH OF A PLANAR GRAPH IN O(N log N) TIME
"... We give an O(n log n) algorithm for computing the girth (shortest cycle) of an undirected nvertex planar graph. Our solution extends to any graph of bounded genus. This improves upon the best previously known algorithms for this problem. ..."
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Cited by 2 (0 self)
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We give an O(n log n) algorithm for computing the girth (shortest cycle) of an undirected nvertex planar graph. Our solution extends to any graph of bounded genus. This improves upon the best previously known algorithms for this problem.
On Graphs Supported by Line Sets
"... For a set S of n lines labeled from 1 to n, we say that S supports an nvertex planar graph G if for every labeling from 1 to n of its vertices, G has a straightline crossingfree drawing with each vertex drawn as a point on its associated line. It is known from previous work [4] that no set of n p ..."
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Cited by 3 (1 self)
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For a set S of n lines labeled from 1 to n, we say that S supports an nvertex planar graph G if for every labeling from 1 to n of its vertices, G has a straightline crossingfree drawing with each vertex drawn as a point on its associated line. It is known from previous work [4] that no set of n
A SEPARATOR THEOREM FOR PLANAR GRAPHS
"... The vertices of any nvertex planar graph 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 2xf x/vertices. We exhibit an algorithm which finds such a partition A, B, C i ..."
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The vertices of any nvertex planar graph 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 2xf x/vertices. We exhibit an algorithm which finds such a partition A, B, C
Computing the Girth of a Planar Graph
 In Proc. 27th International Colloquium on Automata, Languages and Programming ICALP 2000, volume 1853 of LNCS
, 2000
"... The girth of a graph G has been de ned as the length of a shortest cycle of G. We design an O(n 5=4 log n) algorithm for finding the girth of an undirected nvertex planar graph, giving the first o(n 2 ) algorithm for this problem. Our approach combines several techniques such as graph separation, h ..."
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Cited by 6 (0 self)
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The girth of a graph G has been de ned as the length of a shortest cycle of G. We design an O(n 5=4 log n) algorithm for finding the girth of an undirected nvertex planar graph, giving the first o(n 2 ) algorithm for this problem. Our approach combines several techniques such as graph separation
Dominating Sets in Planar Graphs
, 1994
"... Motivated by an application to unstructured multigrid calculations, we consider the problem of asymptotically minimizing the size of dominating sets in triangulated planar graphs. Specifically, we wish to find the smallest ffl such that, for n sufficiently large, every nvertex planar graph cont ..."
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Cited by 8 (0 self)
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Motivated by an application to unstructured multigrid calculations, we consider the problem of asymptotically minimizing the size of dominating sets in triangulated planar graphs. Specifically, we wish to find the smallest ffl such that, for n sufficiently large, every nvertex planar graph
An Optimal Parallel Algorithm for Minimum Spanning Trees in Planar Graphs
"... Abstract. We present an optimal deterministic O(n)work parallel algorithm for finding a minimum spanning tree on an nvertex planar graph. The algorithm runs in O(log n) time on a CRCW PRAM and in O(log n log ∗ n) time on an EREW PRAM. Our results hold for any sparse graph that is closed under tak ..."
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Abstract. We present an optimal deterministic O(n)work parallel algorithm for finding a minimum spanning tree on an nvertex planar graph. The algorithm runs in O(log n) time on a CRCW PRAM and in O(log n log ∗ n) time on an EREW PRAM. Our results hold for any sparse graph that is closed under
A Framework for Drawing Planar Graphs with Curves and Polylines
 J. Algorithms
, 1998
"... We describe a unified framework of aesthetic criteria and complexity measures for drawing planar graphs with polylines and curves. This framework includes several visual properties of such drawings, including aspect ratio, vertex resolution, edge length, edge separation, and edge curvature, as well ..."
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Cited by 18 (4 self)
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as complexity measures such as vertex and edge representational complexity and the area of the drawing. In addition to this general framework, we present algorithms that operate within this framework. Specifically, we describe an algorithm for drawing any nvertex planar graph in an O(n) O(n) grid using
Results 1  10
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7,375