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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 469 (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
Graph Theory
 MATHEMATISCHES FORSCHUNGSINSTITUT OBERWOLFACH REPORT NO. 16/2007
, 2007
"... This week broadly targeted both finite and infinite graph theory, as well as matroids, including their interaction with other areas of pure mathematics. The talks were complemented by informal workshops focussing on specific problems or particularly active areas. ..."
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Cited by 1203 (5 self)
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This week broadly targeted both finite and infinite graph theory, as well as matroids, including their interaction with other areas of pure mathematics. The talks were complemented by informal workshops focussing on specific problems or particularly active areas.
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 629 (44 self)
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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
On the Evolution of Random Graphs
 PUBLICATION OF THE MATHEMATICAL INSTITUTE OF THE HUNGARIAN ACADEMY OF SCIENCES
, 1960
"... his 50th birthday. Our aim is to study the probable structure of a random graph rn N which has n given labelled vertices P, P2,..., Pn and N edges; we suppose_ ..."
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Cited by 3077 (9 self)
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his 50th birthday. Our aim is to study the probable structure of a random graph rn N which has n given labelled vertices P, P2,..., Pn and N edges; we suppose_
The geometry of graphs and some of its algorithmic applications
 Combinatorica
, 1995
"... In this paper we explore some implications of viewing graphs as geometric objects. This approach offers a new perspective on a number of graphtheoretic and algorithmic problems. There are several ways to model graphs geometrically and our main concern here is with geometric representations that r ..."
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Cited by 553 (21 self)
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their geometric images. In this paper we develop efficient algorithms for embedding graphs lowdimensionally with a small distortion. Further algorithmic applications include: 0 A simple, unified approach to a number of problems on multicommodity flows, including the LeightonRae Theorem [29] and some of its
An algorithm for drawing general undirected graphs
 Information Processing Letters
, 1989
"... Graphs (networks) are very common data structures which are handled in computers. Diagrams are widely used to represent the graph structures visually in many information systems. In order to automatically draw the diagrams which are, for example, state graphs, dataflow graphs, Petri nets, and entit ..."
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Cited by 691 (2 self)
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Graphs (networks) are very common data structures which are handled in computers. Diagrams are widely used to represent the graph structures visually in many information systems. In order to automatically draw the diagrams which are, for example, state graphs, dataflow graphs, Petri nets
Depth first search and linear graph algorithms
 SIAM JOURNAL ON COMPUTING
, 1972
"... The value of depthfirst search or "backtracking" as a technique for solving problems is illustrated by two examples. An improved version of an algorithm for finding the strongly connected components of a directed graph and ar algorithm for finding the biconnected components of an undirect ..."
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Cited by 1395 (19 self)
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of an undirect graph are presented. The space and time requirements of both algorithms are bounded by k 1V + k2E d k for some constants kl, k2, and k a, where Vis the number of vertices and E is the number of edges of the graph being examined.
Results 1  10
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