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### Edge-oblique polyhedral graphs

Jens Schreyer, Hansjoachim Walther
2004 Discrete Applied Mathematics
A graph which contains no two edges of a common edge-type is called edge-oblique and if it contains at most z edges of each type it is called z-edge-oblique.  ...  Let G = G(V; E; F) be a polyhedral graph with vertex set V , edge set E and face set F. e = (x; y; ; ÿ) ∈ E(G) denotes an edge incident with the two vertices x; y ∈ V (G); d(x) 6 d(y) and incident with  ...  edge-oblique graphs  ...

### Edge-Oblique Polyhedral Graphs

Jens Schreyer, Hansjoachim Walther
2001 Electronic Notes in Discrete Mathematics
A graph which contains no two edges of a common edge-type is called edge-oblique and if it contains at most z edges of each type it is called z-edge-oblique.  ...  Let G = G(V; E; F) be a polyhedral graph with vertex set V , edge set E and face set F. e = (x; y; ; ÿ) ∈ E(G) denotes an edge incident with the two vertices x; y ∈ V (G); d(x) 6 d(y) and incident with  ...  edge-oblique graphs  ...

### Polyhedral graphs with extreme numbers of types of faces

Hansjoachim Walther
2002 Discrete Applied Mathematics
A face ∈ F of a polyhedral graph G(V; E; F) is an a1; a2; : : : ; a l -face if is an l-gon and the degrees d(xi) of the vertices xi ∈ V incident with in the cyclic order are ai; i = 1; 2; : : : ; l: The  ...  All polyhedral graphs having only one type of faces are listed. It is proved that the set of triangulations having only faces of di erent types is non-empty and ÿnite. ? 2002 Elsevier Science B.V.  ...  A polyhedral graph G is called oblique if all its faces are of di erent type.  ...

### Polyhedral Graphs with Extreme Numbers of Types of Faces

H WALTHER
2000 Electronic Notes in Discrete Mathematics
A face ∈ F of a polyhedral graph G(V; E; F) is an a1; a2; : : : ; a l -face if is an l-gon and the degrees d(xi) of the vertices xi ∈ V incident with in the cyclic order are ai; i = 1; 2; : : : ; l: The  ...  All polyhedral graphs having only one type of faces are listed. It is proved that the set of triangulations having only faces of di erent types is non-empty and ÿnite. ? 2002 Elsevier Science B.V.  ...  A polyhedral graph G is called oblique if all its faces are of di erent type.  ...

### Polyhedral Graphs with Extreme Numbers of Types of Faces

Hansjoachim Walther
1999 Electronic Notes in Discrete Mathematics
A face ∈ F of a polyhedral graph G(V; E; F) is an a1; a2; : : : ; a l -face if is an l-gon and the degrees d(xi) of the vertices xi ∈ V incident with in the cyclic order are ai; i = 1; 2; : : : ; l: The  ...  All polyhedral graphs having only one type of faces are listed. It is proved that the set of triangulations having only faces of di erent types is non-empty and ÿnite. ? 2002 Elsevier Science B.V.  ...  A polyhedral graph G is called oblique if all its faces are of di erent type.  ...

### Page 9593 of Mathematical Reviews Vol. , Issue 2004m [page]

2004 Mathematical Reviews
In this paper it is proved that the set of edge-oblique graphs is finite. Several properties of edge-oblique graphs are proved.  ...  A graph which contains no two edges of the same type is called edge-oblique and if it contains at most z edges of each type it is called z-edge-oblique.  ...

### Polyhedral graphs with restricted number of faces of the same type

M. Voigt, H. Walther
2002 Discrete Mathematics
Let G = G(V; E; F) be a polyhedral graph with vertex set V , edge set E and face set F.  ...  We consider polyhedral graphs where the number of faces of each type is restricted by z. We prove that there is only a ÿnite number of such graphs.  ...  Introduction All graphs considered in the sequel are polyhedral graphs, i.e. they are planar and three-connected. Vertex set, edge set and face set are denoted by V , E and F, respectively.  ...

### Almost every graph is vertex-oblique

Jens Schreyer
2007 Discrete Mathematics
We will show that almost every graph G ∈ G(n, p) is vertex-oblique, if the probability p for each edge to appear in G is within certain bounds.  ...  The type of a vertex v of a graph G is the ordered degree sequence of the vertices adjacent to v. The graph G is called vertex-oblique if it contains no two vertices of the same type.  ...  well as Frank Göring who saw the connection to the graph isomorphism problem.  ...

### Contents

2007 Discrete Mathematics
Schreyer Almost every graph is vertex-oblique 983  ...  TuhárskyLight stars in large polyhedral maps on surfaces 1001M. VoigtA non-3-choosable planar graph without cycles of length 4 and 5 1013M.  ...

### Perceptual grouping of line features in 3-D space: a model-based framework

In Kyu Park, Kyoung Mu Lee, Sang Uk Lee
2004 Pattern Recognition
The Gestalt graph is then decomposed into a few subgraphs, yielding appropriate groups of features.  ...  In this paper, we propose a novel model-based perceptual grouping algorithm for the line features of 3-D polyhedral objects.  ...  If a small number of edges (usually less than 3) divide the graph into more than two subgraphs and the size of the children subgraphs are large enough, then the edges are removed from the graph, making  ...

### Vertex-oblique graphs

Jens Schreyer, Hansjoachim Walther, Leonid S. Mel'nikov
2007 Discrete Mathematics
We call the graph G vertex-oblique if there are no two vertices in V (G) which are of the same vertex-type. We will show that the set of vertex-oblique graphs of arbitrary connectivity is infinite.  ...  Let x be a vertex of a simple graph G. The vertex-type of x is the lexicographically ordered degree sequence of its neighbors.  ...  It remains to investigate whether the same is true in the vertex-oblique case. • Should there only be finite many polyhedral vertex-oblique graphs, are there at least infinitely many vertex-oblique graphs  ...

### Robust piecewise-planar 3D reconstruction and completion from large-scale unstructured point data

Anne-Laure Chauve, Patrick Labatut, Jean-Philippe Pons
2010 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition
A major contribution of our work is an adaptive decomposition of 3D space induced by planar primitives, namely a polyhedral cell complex.  ...  This labeling problem is handled within the framework of minimum s − t cut on the cell-adjacency graph G = (V, E) of the partition: the vertices V are the cells of the polyhedral complex while the edges  ...  More precisely, we consider the directed adjacency graph with a (directed) edge corresponding to each oriented facet of the complex.  ...

### Minimal graphs of a torus, a projective plane and spheres and some properties of minimal graphs of homotopy classes

Alexander V. Ivashchenko, Yeong-Nan Yeh
1994 Discrete Mathematics
Contractible transformations of graphs consist of contractible gluing and deleting of vertices and edges of graphs. They partition all graphs into the family of homotopy classes.  ...  We also describe the minimal graphs of a projective plane, a torus and a sphere.  ...  oblique) edges and obtain the graph H, which is minimal, and F(G)=F(M)=O. Fig. 3.  ...

### Realistic analytical polyhedral MRI phantoms

Tri M. Ngo, George S. K. Fung, Shuo Han, Min Chen, Jerry L. Prince, Benjamin M. W. Tsui, Elliot R. McVeigh, Daniel A. Herzka
2015 Magnetic Resonance in Medicine
Simulations of 3D/2D brain and 2D torso cine acquisitions produced realistic reconstructions free of high frequency edge aliasing as compared to equivalent voxelized/rasterized phantoms.  ...  Realistic anthropomorphic polyhedral brain and torso phantoms were constructed and their use in simulated 3D/2D MRI acquisitions was described.  ...  Edge differences were more pronounced in the finite slice simulation due to partial volume effects of oblique edges that were not modeled in the rasterized phantom.  ...

### Curved Buildings Reconstruction from Airborne LiDAR Data by Matching and Deforming Geometric Primitives [article]

Jingwei Song, Shaobo Xia, Jun Wang, Dong Chen
2020 arXiv   pre-print
Specifically, an embedded deformation (ED) graph is constructed via downsampling the initial model.  ...  Then, the point-to-model displacements are minimized by adjusting node parameters in the ED graph based on our objective function.  ...  The connected edges constitute the surfaces of polyhedral building roofs, the main structures of typical polyhedral buildings.  ...
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