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121
Triangular embeddings of complete graphs from graceful labellings of paths
, 2006
"... We show that to each graceful labelling of a path on 2s + 1 vertices, s ≥ 2, there corresponds a current assignment on a 3valent graph which generates at least 2 2s cyclic oriented triangular embeddings of a complete graph on 12s + 7 vertices. We also show that in this correspondence, two distinct ..."
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Cited by 10 (0 self)
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We show that to each graceful labelling of a path on 2s + 1 vertices, s ≥ 2, there corresponds a current assignment on a 3valent graph which generates at least 2 2s cyclic oriented triangular embeddings of a complete graph on 12s + 7 vertices. We also show that in this correspondence, two distinct
CommonFace Embeddings of Planar Graphs
, 2001
"... Given a planar graph G and a sequence C1,...,Cq, where each Ci is a family of vertex subsets of G, we wish to find a plane embedding of G, if any exists, such that for each i ∈ {1,..., q}, there is a face Fi in the embedding whose boundary contains at least one vertex from each set in Ci. This probl ..."
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Given a planar graph G and a sequence C1,...,Cq, where each Ci is a family of vertex subsets of G, we wish to find a plane embedding of G, if any exists, such that for each i ∈ {1,..., q}, there is a face Fi in the embedding whose boundary contains at least one vertex from each set in Ci
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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Valiant's results by showing that an Nnode planar graph has a planarembedding with area O(NF), where F is a bound on the path length from any node to the exterior face. In particular, an outerplanar graph can be embedded without crossings in linear area. This bound is tight, up to constant factors
Existence of polyhedral embeddings of graphs is NPcomplete
"... It is proved that the decision problem about existence of an embedding of facewidth 3 of a given graph is NPcomplete. A similar result is proved for some related decision problems. This solves a problem raised by Neil Robertson. ..."
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It is proved that the decision problem about existence of an embedding of facewidth 3 of a given graph is NPcomplete. A similar result is proved for some related decision problems. This solves a problem raised by Neil Robertson.
Existence of polyhedral embeddings of graphs
 Combinatorica
"... It is proved that the decision problem about the existence of an embedding of facewidth 3 of a given graph is NPcomplete. A similar result is proved for some related decision problems. This solves a problem raised by Neil Robertson. 1 ..."
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Cited by 1 (1 self)
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It is proved that the decision problem about the existence of an embedding of facewidth 3 of a given graph is NPcomplete. A similar result is proved for some related decision problems. This solves a problem raised by Neil Robertson. 1
The many faces of ocneanu cells
 Nuclear Phys. B
"... We define generalised chiral vertex operators covariant under the Ocneanu “double triangle algebra” A, a novel quantum symmetry intrinsic to a given rational 2d conformal field theory. This provides a chiral approach, which, unlike the conventional one, makes explicit various algebraic structures e ..."
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Cited by 61 (5 self)
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encountered previously in the study of these theories and of the associated critical lattice models, and thus allows their unified treatment. The triangular Ocneanu cells, the 3jsymbols of the weak Hopf algebra A, reappear in several guises. With A and its dual algebra Â one associates a pair of graphs, G
Sampling Eulerian orientations of triangular . . .
, 2007
"... We consider the problem of sampling from the uniform distribution on the set of Eulerian orientations of subgraphs of the triangular lattice. Although it is known that this can be achieved in polynomial time for any graph, the algorithm studied here is more natural in the context of planar Eulerian ..."
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We consider the problem of sampling from the uniform distribution on the set of Eulerian orientations of subgraphs of the triangular lattice. Although it is known that this can be achieved in polynomial time for any graph, the algorithm studied here is more natural in the context of planar Eulerian
Hexahedral mesh generation using the embedded Voronoi graph
 In Proceedings of the 7th International Meshing Roundtable
, 1999
"... This work presents a new approach for automatic hexahedral meshing, based on the embedded Voronoi graph. The embedded Voronoi graph contains the full symbolic information of the Voronoi diagram and the medial axis of the object, and a geometric approximation to the real geometry. The embedded Vorono ..."
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Cited by 30 (0 self)
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volume, even if its medial axis is degenerate. The embedded Voronoi graph provides complete information regarding proximity and adjacency relationships between the entities of the volume. Hence, decomposition faces are determined unambiguously, without any further geometric computations. The sub
Planar Embeddings with Small and Uniform Faces
, 2014
"... Motivated by finding planar embeddings that lead to drawings with favorable aesthetics, we study the problems MINMAXFACE and UNIFORMFACES of embedding a given biconnected multigraph such that the largest face is as small as possible and such that all faces have the same size, respectively. We pro ..."
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Motivated by finding planar embeddings that lead to drawings with favorable aesthetics, we study the problems MINMAXFACE and UNIFORMFACES of embedding a given biconnected multigraph such that the largest face is as small as possible and such that all faces have the same size, respectively. We
Results 1  10
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121