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An equitable partition for a distance-regular graph of negative type

Štefko Miklavič
2005 Journal of combinatorial theory. Series B (Print)  
Let denote a distance-regular graph with diameter d 3. Assume has classical parameters We investigate the extent to which is 1-homogeneous in the sense of Nomura.  ...  We show that either is 1-homogeneous, or else has a certain equitable partition of its vertex set which involves 4d − 1 cells.  ...  Terwilliger for his careful reading of the earlier versions of this paper and for his comments.  ... 
doi:10.1016/j.jctb.2005.02.007 fatcat:aosit4vejng4beerbh3b7am3xa

Page 4600 of Mathematical Reviews Vol. , Issue 82k [page]

1982 Mathematical Reviews  
In this paper the author constructs a distance-regular graph with intersection array {10,8,8,2;1,1,4,5} amd the associated near octagon.  ...  Furthermore, if the intersection array of G has the form {s(¢+1),st,st,s(t—t;),---,s(t—ta-1); 1l,t4+1,---,tg-,+1,¢4+1}, then the vertices and maximal cliques constitute what has been called a regular near  ... 

Image partitioning into convex polygons

Liuyun Duan, Florent Lafarge
2015 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)  
Our algorithm partitions images into convex polygons. It presents several interesting properties in terms of geometric guarantees, region compactness and scalability.  ...  The overall strategy consists in building a Voronoi diagram that conforms to preliminarily detected line-segments, before homogenizing the partition by spatial point process distributed over the image  ...  The authors thank Lionel Laurore, Justin Hyland, Véronique Poujade and Frédéric Trastour for technical discussions and satellite datasets.  ... 
doi:10.1109/cvpr.2015.7298931 dblp:conf/cvpr/DuanL15 fatcat:lwh5oo6btba5pifcqopkqvrbxm

European Journal of Combinatorics Contents, Volume 26

2005 European journal of combinatorics (Print)  
-W., An inequality for regular near polygons . . . . . . . . . . . . . . . . 227 CHEN, W.Y.C., DENG, E.Y.P. and DU, R.R.X., Reduction of m-regular noncrossing partitions . . . . . . . . . . . . . 237 HAN  ...  -F., KWAK, J.H. and NEDELA, R., Regular embeddings of complete multipartite graphs . . . . . . . . . . . . . . 505 LI, C.H. andŠIRÁŇ, J., Regular maps whose groups do not act faithfully on vertices, edges  ... 
doi:10.1016/s0195-6698(05)00128-9 fatcat:fb5uilehgvgzxgmj7sfw4lm5hq


Jun-Cheol Pyo
2012 Bulletin of the Korean Mathematical Society  
piece of finite total curvature and is asymptotic to a finite number of vertical planes; the last one is a 2-parameter family of minimal surfaces which fill H 2 × R by finite Scherk's towers.  ...  The first one is a 1-parameter family of minimal surfaces which is asymptotic to a horizontal plane and a vertical plane; the second one is a 2-parameter family of minimal surfaces which has a fundamental  ...  Morrey's result [9] requires the ambient manifold M 3 to be complete and homogeneously regular.  ... 
doi:10.4134/bkms.2012.49.5.1089 fatcat:ugyos2fuffeq5aq7f2qavozefy

Complete optimal deployment patterns for full-coverage and k-connectivity (k≤6) wireless sensor networks

Xiaole Bai, Dong Xuan, Ziqiu Yun, Ten H. Lai, Weijia Jia
2008 Proceedings of the 9th ACM international symposium on Mobile ad hoc networking and computing - MobiHoc '08  
We propose a new deployment-polygon based methodology, and prove their optimality among regular patterns when Rc/Rs ≥ 1.  ...  We conjecture that our patterns are globally optimal to achieve full coverage and threeconnectivity, and full coverage and five-connectivity, under all ranges of Rc/Rs.  ...  Fig. 1 shows the deployment graphs of two possible regular deployment achieving 3 and 5-connectivity, respectively.  ... 
doi:10.1145/1374618.1374672 dblp:conf/mobihoc/BaiXYLJ08 fatcat:d3qh27uvrbgelci6ce3sbm7e2y

European Journal of Combinatorics Index, Volume 26

2005 European journal of combinatorics (Print)  
., An inequality for regular near polygons . . . . . . . . . . . . . . . . 227 THOMAS, R. and WOLLAN, P., An improved linear edge bound for graph linkages . . . . . . . . . . . . . . . . . 309 BEDNARSKA  ...  ., KWAK, J.H. and WANG, K., Classifying cubic symmetric graphs of order 8 p or 8 p 2 . . . . . . . . . . . . 1033 GARCIA-DOMINGO, J.L. and SORIA, J., A decreasing rearrangement for functions on homogeneous  ... 
doi:10.1016/s0195-6698(05)00129-0 fatcat:vuytixhru5bupfpbxzzanswabu


2000 International journal of computational geometry and applications  
This approach handles optimization criteria such as density, angles and regularity, too.  ...  and satis es prescribed local density constraints.  ...  M ohring and K. Weihe for many fruitful discussions, and G. Krause for providing us with the nite element preprocessor ISAGEN and instances from the automobile industry. Finally, we thank A.  ... 
doi:10.1142/s0218195900000176 fatcat:ixtmu3foxjhpviunumpphrisai

Distance-regular graphs [article]

Edwin R. van Dam, Jack H. Koolen, Hajime Tanaka
2016 arXiv   pre-print
We present an introduction to distance-regular graphs for the reader who is unfamiliar with the subject, and then give an overview of some developments in the area of distance-regular graphs since the  ...  This is a survey of distance-regular graphs.  ...  Let Γ be a thick regular near polygon with diameter D and head h.  ... 
arXiv:1410.6294v2 fatcat:s6kq2ydbtzaldcwjk4qgawfawu

On approaches to polygonal decomposition for hierarchical image representation

Narendra Ahuja
1983 Computer Vision Graphics and Image Processing  
Approaches to polygonal decomposition for hierarchical image representation are described.  ...  Triangular and square quad trees are appropriate for the triangular and square grids, whereas trees of order 7 are necessary for the hexagonal grid. 200  ...  Navy, and U.S. Air Force) under Contract NO001479-C-0424 is gratefully acknowledged, as is the help of Mary Foster in preparing this paper.  ... 
doi:10.1016/0734-189x(83)90043-9 fatcat:zvqv3zuxnra5hnumebngc7aufq

Polygonal Building Segmentation by Frame Field Learning [article]

Nicolas Girard, Dmitriy Smirnov, Justin Solomon, Yuliya Tarabalka
2021 arXiv   pre-print
This additional objective improves segmentation quality by leveraging multi-task learning and provides structural information that later facilitates polygonization; we also introduce a polygonization algorithm  ...  Our code is available at  ...  We can see our method provides the missing information needed to resolve ambiguous cases for polygonization and outputs more regular polygons.  ... 
arXiv:2004.14875v2 fatcat:iaql4iwbvrawrfcaemgeyt2b7q

Indexing and Browsing Digital Maps with Intelligent Thumbnails [chapter]

Christoph Schlieder, Thomas Vögele
2002 Advances in Spatial Data Handling  
connection graph.  ...  To make the thumbnail exchangeable in a distributed and heterogeneous environment, the underlying Standard Reference Tessellation (SRT) is qualitatively abstracted from a polygonal representation to a  ...  The projection of the polygonal footprint of a geographic feature onto a regular, homogeneous grid is depicted in Fig 2.  ... 
doi:10.1007/978-3-642-56094-1_6 fatcat:qy6rqduj2bd2bjpl4ca7rgezji

Periodic boundary conditions on the pseudosphere

F Sausset, G Tarjus
2007 Journal of Physics A: Mathematical and Theoretical  
dynamics of particles on the pseudosphere and the study of classical spins on hyperbolic lattices.  ...  Starting from the common case of periodic boundary conditions in the Euclidean plane, we introduce all the needed mathematical notions and sketch a classification of periodic boundary conditions on the  ...  the associated tiling (we only consider regular metric fundamental polygons and regular tilings), -the pairing of the sides, which can be achieved by using the graph formalism detailed above.  ... 
doi:10.1088/1751-8113/40/43/004 fatcat:czy2e2wnuff7hoftpsvl57p55y

Deep Learning and Adaptive Graph-Based Growing Contours for Agricultural Field Extraction

Matthias P. Wagner, Natascha Oppelt
2020 Remote Sensing  
Monitoring schemes and national cadasters provide a rich source of information but their maintenance and regular updating is costly and labor-intensive.  ...  Automatized mapping of fields based on remote sensing imagery may aid in this task and allow for a faster and more regular observation.  ...  Acknowledgments: We thank the students and student assistants who carried out in-situ mapping campaigns and helped produce and update the reference data.  ... 
doi:10.3390/rs12121990 fatcat:tof5iu3tdzcpxhdabwxkjevgry

A new approach for a topographic feature-based characterization of digital elevation data

Eric Saux, R�my Thibaud, Ki-Joune Li, Min-Hwan Kim
2004 Proceedings of the 12th annual ACM international workshop on Geographic information systems - GIS '04  
Firstly, a segmentation process extracts homogeneous morphological areas bounded by critical lines and points.  ...  Triangular Irregular Network (TIN) and Regular Square Grid (RSG) are widely used for representing 2.5 dimensional spatial data.  ...  In such a graph, each node and edge may represent a polygon (resp. a feature point) and the adjacency between two polygons (resp. two feature points).  ... 
doi:10.1145/1032222.1032235 dblp:conf/gis/SauxTLK04 fatcat:edffgajnmnhilixufaky55dfv4
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