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215
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 ..."
Abstract

Cited by 628 (44 self)
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as follows: ffl We devise a model for dynamic graph algorithms, based on performing queries and updates on an implicit representation of the drawing, and we show its applications. ffl We present several efficient dynamic drawing algorithms for trees, seriesparallel digraphs, planar stdigraphs, and planar
Balanced Circle Packings for Planar Graphs
"... Abstract. In this paper, we study balanced circle packings and circlecontact representations for planar graphs, where the ratio of the largest circle’s diameter to the smallest circle’s diameter is polynomial in the number of circles. We provide a number of positive and negative results for the exi ..."
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Abstract. In this paper, we study balanced circle packings and circlecontact representations for planar graphs, where the ratio of the largest circle’s diameter to the smallest circle’s diameter is polynomial in the number of circles. We provide a number of positive and negative results
Primaldual Circle packing of Planar Maps
"... This work is based on Mohar [1]'s recent algorithm for circle packing for the Euclean case. We implement his polynomial time algorithm for constructing primaldual circle packings of almost 3connected planar maps. We have improved Mohar's algorithm and have been able to get near an order ..."
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of magnitude speed up for large graphs. We describe our implementation in C/C++ style pseudocode. Keywords Primaldual circle packing, contact graph, Graph Drawing, Euclean surface. I. Introduction Circle packing of graphs has many applications in the area of computer graphics and computational geometry
Circle Planarity of Level Graphs
, 2004
"... In this thesis we generalise the notion of level planar graphs in two directions: track planarity and radial planarity. Our main results are linear time algorithms both for the planarity test and for the computation of an embedding, and thus a drawing. Our algorithms use and generalise PQtrees, whi ..."
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Cited by 1 (1 self)
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In this thesis we generalise the notion of level planar graphs in two directions: track planarity and radial planarity. Our main results are linear time algorithms both for the planarity test and for the computation of an embedding, and thus a drawing. Our algorithms use and generalise PQ
Planar Packing of Binary Trees
"... Abstract. In the graph packing problem we are given several graphs and have to map them into a single host graph G such that each edge of G is used at most once. Much research has been devoted to the packing of trees, especially to the case where the host graph must be planar. More formally, the pro ..."
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of diameter four and two isomorphic trees. We make a step forward and prove the hypothesis for any two binary trees. The proof is algorithmic and yields a linear time algorithm to compute a plane packing, that is, a suitable twoedgecolored host graph along with a planar embedding for it. In addition we can
Harmonic Functions On Planar And Almost Planar Graphs And Manifolds, Via Circle Packings
"... . The circle packing theorem is used to show that on any bounded valence transient planar graph there exists a non constant, harmonic, bounded, Dirichlet function. If P is a bounded circle packing in R 2 whose contacts graph is a bounded valence triangulation of a disk, then, with probability 1 , ..."
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. The circle packing theorem is used to show that on any bounded valence transient planar graph there exists a non constant, harmonic, bounded, Dirichlet function. If P is a bounded circle packing in R 2 whose contacts graph is a bounded valence triangulation of a disk, then, with probability 1
Circle packings of maps in polynomial time
 Eur. J. Comb
, 1997
"... The AndreevKoebeThurston circle packing theorem is generalized and improved in two ways. First, we get simultaneous circle packings of the map and its dual map so that, in the corresponding straightline representations of the map and the dual, any two edges dual to each other are perpendicular. N ..."
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Cited by 11 (2 self)
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. Necessary and sufficient condition for a map to have such a primaldual circle packing representation in a surface of constant curvature is that its universal cover is 3connected (the map has no “planar” 2separations). Secondly, an algorithm is obtained that given a map M and a rational number ε>0
ON A CONJECTURE OF LOVÁSZ ON CIRCLEREPRESENTATIONS OF SIMPLE 4REGULAR PLANAR GRAPHS
 JOURNAL OF COMPUTATIONAL GEOMETRY
, 2012
"... Lovász conjectured that every connected 4regular planar graph G admits a realization as a system of circles, i.e., it can be drawn on the plane utilizing a set of circles, such that the vertices of G correspond to the intersection and touching points of the circles and the edges of G are the arc ..."
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Lovász conjectured that every connected 4regular planar graph G admits a realization as a system of circles, i.e., it can be drawn on the plane utilizing a set of circles, such that the vertices of G correspond to the intersection and touching points of the circles and the edges of G
CIRCLE PACKINGS OF MAPS  THE EUCLIDEAN CASE
"... In an earlier work, the author extended the AndreevKoebeThurston circle packing theorem. Additionally, a polynomial time algorithm for constructing primaldual circle packings of arbitrary (essentially) 3connected maps was found. In this note, additional details concerning surfaces of constant c ..."
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In an earlier work, the author extended the AndreevKoebeThurston circle packing theorem. Additionally, a polynomial time algorithm for constructing primaldual circle packings of arbitrary (essentially) 3connected maps was found. In this note, additional details concerning surfaces of constant
Kissing Circle Representation
, 2002
"... #44 Is every zonohedron 3colorable when viewed as a planar map? This question arose out of work described in [RSW01]. An equivalent question, under a different guise, is posed in [FHNS00]: Is the arrangement graph of great circles on the sphere 3colorable? Assume no three circles meet at a point, ..."
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#44 Is every zonohedron 3colorable when viewed as a planar map? This question arose out of work described in [RSW01]. An equivalent question, under a different guise, is posed in [FHNS00]: Is the arrangement graph of great circles on the sphere 3colorable? Assume no three circles meet at a point
Results 1  10
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