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Edge Partitions of Complete Geometric Graphs (Part 2) [article]

Oswin Aichholzer, Johannes Obenaus, Joachim Orthaber, Rosna Paul, Patrick Schnider, Raphael Steiner, Tim Taubner, Birgit Vogtenhuber
2021 arXiv   pre-print
Recently, the second and third author showed that complete geometric graphs on 2n vertices in general cannot be partitioned into n plane spanning trees.  ...  Building up on this work, in this paper, we initiate the study of partitioning into beyond planar subgraphs, namely into k-planar and k-quasi-planar subgraphs and obtain first bounds on the number of subgraphs  ...  Acknowledgements We thank the organizers and participants of the 5 th DACH Workshop on Arrangements and Drawings, that took place in March 2021 (online) and was funded by Deutsche Forschungsgemeinschaft  ... 
arXiv:2112.08456v1 fatcat:3uchv25xufbzpcwspaz3mgw4ka

Edge Partitions of Complete Geometric Graphs (Part 1) [article]

Johannes Obenaus, Joachim Orthaber
2021 arXiv   pre-print
In this paper, we disprove the long-standing conjecture that any complete geometric graph on 2n vertices can be partitioned into n plane spanning trees.  ...  We fully characterize which bumpy wheels can and in particular which cannot be partitioned into plane spanning trees (or even into arbitrary plane subgraphs), including a complete description of all possible  ...  Edge Partitions of Complete Geometric Graphs (Part 1)Figure13Full partition of BW9,3 into 14 plane spanning trees according to the construction in case 1 of Theorem 15 (generated by the computer assisted  ... 
arXiv:2108.05159v2 fatcat:sgxisi7iibgmderhhujbcndbfm

Edge Partitions of Complete Geometric Graphs

Oswin Aichholzer, Johannes Obenaus, Joachim Orthaber, Rosna Paul, Patrick Schnider, Raphael Steiner, Tim Taubner, Birgit Vogtenhuber, Xavier Goaoc, Michael Kerber
2022
In this paper, we disprove the long-standing conjecture that any complete geometric graph on 2n vertices can be partitioned into n plane spanning trees.  ...  Finally, we initiate the study of partitions into beyond planar subgraphs, namely into k-planar and k-quasi-planar subgraphs and obtain first bounds on the number of subgraphs required in this setting.  ...  Acknowledgements Research on this work has been initiated in March 2021, at the 5 th research workshop of the collaborative D-A-CH project Arrangements and Drawings, which was funded by the DFG, the FWF  ... 
doi:10.4230/lipics.socg.2022.6 fatcat:kvt44ep7ufdero2737a4ch7q3y

Parallel Tree Contraction Part 2: Further Applications

Gary L. Miller, John H. Reif
1991 SIAM journal on computing (Print)  
These shared edges will not be edges from G, the original graph, but rather, from new edges called virtual edges. There will be exactly two copies of each virtual edge.  ...  An edge from 2 to y of C will be an original edge from G if z and y share exactly one trivial bridge; otherwise, the edge will be a virtual edge.  ... 
doi:10.1137/0220070 fatcat:i7bjji4aefes5ayetgrt2ywdfq

Symbolic OBDD Assembly Sequence Planning Algorithm Based on Unordered Partition with 2 Parts of a Positive Integer [chapter]

Zhoubo Xu, Tianlong Gu, Rongsheng Dong
2012 IFIP Advances in Information and Communication Technology  
To convert the decomposition of assembly liaison graph into solving unordered partition with 2 parts of positive integer N, a transformation method from subassembly of the assembly to positive integer  ...  with 2 parts of a positive integer is proposed.  ...  Acknowledgements This work hav been supported by National Natural Science Foundation of China (61100025,60963010,61063002) and Science Foundation of Guangxi Key Laboratory of Trusted Software (No. kx201119  ... 
doi:10.1007/978-3-642-32891-6_29 fatcat:fw5qhq3h2reodjm6j5hvh4phji

Perceptual influence of elementary three-dimensional geometry: (2) fundamental object parts

Minija Tamosiunaite, Rahel M. Sutterlütti, Simon C. Stein, Florentin Wörgötter
2015 Frontiers in Psychology  
Kerstin Fischer provided valuable contributions to the language parts of this study and Dr. Marina Wimmer discussed with us the developmental background.  ...  ., 2013) with graph edges showing how voxels are neighbors. (B2) Conventional definition of convex and concave configurations.  ...  ., 2013) which capture the scene geometry by their neighborhood relations (graph-edges in Figure 1B1 ).  ... 
doi:10.3389/fpsyg.2015.01427 pmid:26441797 pmcid:PMC4585234 fatcat:uhdlsiym3fbfvgg7jqfc6l4kqa

Contextual Part Analogies in 3D Objects

L. Shapira, S. Shalom, A. Shamir, D. Cohen-Or, H. Zhang
2009 International Journal of Computer Vision  
Our matching function is based on bipartite graph matching and is computed using a flow algorithm which takes into account both local geometrical fea-L. Shapira ( ) · D.  ...  By partitioning an object into meaningful parts and finding analogous parts in other objects, not necessarily of the same type, many analysis and modeling tasks could be enhanced.  ...  Fig. 1 ( 1 Color online) Contextual part analogies: (a) Fig. 2 2 Sample Fig. part in the model is assigned a local signature composed of its geometrical attributes.  ... 
doi:10.1007/s11263-009-0279-0 fatcat:fa72qnyqkrbvhbb2xrxnxckdje

Managing Extended Producer Responsibility using PLM Part 2: Identification of Joints for End-of-life Treatment Planning

Nikhil Joshi, Debasish Dutta
2008 Computer-Aided Design and Applications  
In this second part, we outline a methodology that can enable case-by-case selection of the treatment strategy for incoming end-of-life products.  ...  In this two part paper, we present methodologies for OEMs to use the Product Lifecycle Management (PLM) framework to effectively meet the challenges posed by these regulations.  ...  Fig. 1 : 1 Partition lattice (π 4 ) for a four part product. Fig. 2 : 2 Tasks in planning end-of-life treatment strategy. Fig. 3 : 3 Example part with "screw" joints.  ... 
doi:10.3722/cadaps.2008.764-773 fatcat:uh3p5aym3zb45b76cwlqqxv3hy

Topological finiteness properties of monoids. Part 2: special monoids, one-relator monoids, amalgamated free products, and HNN extensions [article]

Robert D. Gray, Benjamin Steinberg
2020 arXiv   pre-print
In particular we show that all such monoids are of type F_∞ (and FP_∞), and that when r is not a proper power, then the monoid has geometric and cohomological dimension at most 2.  ...  We also obtain results which relate the geometric and cohomological dimensions of such a monoid to those of its group of units.  ...  We can then define a directed bipartite graph T with one part given by the M 1 -orbits and the other part given by the M 2 -orbits.  ... 
arXiv:1805.03413v2 fatcat:xntgd4u7a5aazjqkbv23vlfrpe

Burling graphs revisited, part II: Structure [article]

Pegah Pournajafi, Nicolas Trotignon
2022 arXiv   pre-print
We recall an equivalent definition of Burling graphs from the first part of this work: the graphs derived from a tree. We then give several structural properties of derived graphs.  ...  These graphs have attracted some attention because they have geometric representations and because they provide counter-examples to several conjectures about bounding the chromatic number in classes of  ...  In the first part of this work [7] , we gave several equivalent definitions of Burling graphs and geometrical charactreziations of Burling graphs.  ... 
arXiv:2106.16089v3 fatcat:sj25eae4wralvd6c23i3q7ig2e

Relative Position Computation for Assembly Planning With Planar Toleranced Parts

Yaron Ostrovsky-Berman, Leo Joskowicz
2006 The international journal of robotics research  
We describe efficient algorithms for computing the sensitivity of part positioning to variations in part geometries, and for incorporating these computations into the geometric core of existing assembly  ...  We conclude that geometric computation for assembly planning with tolerance parts is time efficient and practical.  ...  A cycle of N c parts has exactly N c − 2 edges of weight 3, one edge of weight 2, and one edge of weight 1.  ... 
doi:10.1177/0278364906060133 fatcat:skpzzk6nj5hsjl63ohomlap4lm

Relation between part position and kinematic freedom: An expository survey

Avinash Dawari, Dibakar Sen
2010 Mechanism and Machine Theory  
The physical contact between the parts in an assembly reduces the degrees of freedom of the parts involved.  ...  Over 100 papers are reviewed in the areas of relative part positioning and deriving kinematic information from parts or assemblies.  ...  The positioning of parts causes some of the low level geometric entities like faces, edges, and vertices of the parts to be in contact.  ... 
doi:10.1016/j.mechmachtheory.2009.09.011 fatcat:wwduf4qzgfbj5pu2maxvbnvbbm

The jump set under geometric regularisation. Part 2: Higher-order approaches

T. Valkonen
2017 Journal of Mathematical Analysis and Applications  
We also study the limiting behaviour of the singular part of Du, as the second parameter of TGV 2 goes to zero.  ...  Now, in this Part 2, we extend the technique to higher-order regularisers.  ...  and Applications in Biomedical Sciences" of the Austrian Science Fund (FWF).  ... 
doi:10.1016/j.jmaa.2017.04.037 fatcat:qtit7cqm3nhxlm7cihgzsor6zi

A Study of Parts-Based Object Class Detection Using Complete Graphs

Martin Bergtholdt, Jörg Kappes, Stefan Schmidt, Christoph Schnörr
2009 International Journal of Computer Vision  
Along this line of research, we present a practicable and expandable probabilistic framework for parts-based object class representation, enabling the detection of rigid and articulated object classes  ...  Hampered by the omnipresent confusing information due to clutter and occlusion, the focus has shifted from holistic approaches for object detection to representations of individual object parts linked  ...  We also thank the anonymous reviewers for their detailed and constructiv criticism that helped to improve the original version of the manuscript.  ... 
doi:10.1007/s11263-009-0209-1 fatcat:y5w5rjant5fx5d75x7wej6x2nm

Varieties of Nodal surfaces, coding theory and Discriminants of cubic hypersurfaces. Part 1: Generalities and nodal K3 surfaces. Part 2: Cubic Hypersurfaces, associated discriminants. Part 3: Nodal quintics. Part 4: Nodal sextics [article]

Fabrizio Catanese, Yonghwa Cho, Stephen Coughlan, Davide Frapporti, Alessandro Verra, Michael Kiermaier
2022 arXiv   pre-print
For degree d=6, our main result is based on some novel auxiliary results: 1) the study of the half-even sets of nodes on sextic surfaces, 2) the investigation of discriminants of cubic hypersurfaces X,  ...  In the fourth part we show that a 'Togliatti-like' description holds for surfaces of degree 6 with the maximum number of nodes= 65: they are discriminants of cubic hypersurfaces in P^6 with 31 (respectively  ...  We denote by E the set of edges. The number of vertices of the Petersen graph is then 10 and the number of edges is 15.  ... 
arXiv:2206.05492v2 fatcat:etorsx2kcjgblflezmc347ntze
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