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The geometric thickness of low degree graphs

2004
*
Proceedings of the twentieth annual symposium on Computational geometry - SCG '04
*

We prove that

doi:10.1145/997817.997868
dblp:conf/compgeom/DuncanEK04
fatcat:krqz663n7nfi5myff5cfhed5ri
*the**geometric**thickness**of**graphs*whose maximum*degree*is no more than four is two. ...*The*results have implications in*graph*theory,*graph*drawing, and VLSI design. ... In a recent paper on*geometric**thickness*[14] , one*of**the*authors posed as an open problem bounding*the**geometric**thickness**of*a*graph*as a function*of*its*degree*. ...##
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The Geometric Thickness of Low Degree Graphs
[article]

2003
*
arXiv
*
pre-print

We prove that

arXiv:cs/0312056v1
fatcat:lwkf66wodzgpbf5oqnxkiurxpq
*the**geometric**thickness**of**graphs*whose maximum*degree*is no more than four is two. All*of*our algorithms run in O(n) time, where n is*the*number*of*vertices in*the**graph*. ... We also show a variation using orthogonal edges for maximum*degree*four*graphs*that also uses an n x n grid.*The*results have implications in*graph*theory,*graph*drawing, and VLSI design. ... In a recent paper on*geometric**thickness*[14] , one*of**the*authors posed as an open problem bounding*the**geometric**thickness**of*a*graph*as a function*of*its*degree*. ...##
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Separating Thickness from Geometric Thickness
[article]

2003
*
arXiv
*
pre-print

We show that

arXiv:math/0204252v2
fatcat:w3r7t2kabfd2dcvdro3p3bjgbm
*graph*-theoretic*thickness*and*geometric**thickness*are not asymptotically equivalent: for every t, there exists a*graph*with*thickness*three and*geometric**thickness*>= t. ... Do random four-regular*graphs*have bounded expected*geometric**thickness*? More generally, do bounded*degree**graphs*have bounded*geometric**thickness*? ... Is there a 2inductive*graph*with*geometric**thickness*greater than two? Can*the**geometric**thickness**of*such*graphs*be unbounded? ...##
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Separating Thickness from Geometric Thickness
[chapter]

2002
*
Lecture Notes in Computer Science
*

We show that

doi:10.1007/3-540-36151-0_15
fatcat:skiqtex56zcutpos2ghzfpyw7a
*graph*-theoretic*thickness*and*geometric**thickness*are not asymptotically equivalent: for every t, there exists a*graph*with*thickness*three and*geometric**thickness*≥ t. ... Do random four-regular*graphs*have bounded expected*geometric**thickness*? More generally, do bounded*degree**graphs*have bounded*geometric**thickness*? ... Can we find good upper bounds for*geometric**thickness*as a combination*of**the**graph*-theoretic*thickness*and a slowly growing function*of**the**graph*size? ...##
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Degree correlations in random geometric graphs

2012
*
Physical Review E
*

*The*prototypical spatial net- work we assume is

*the*Random

*Geometric*

*Graph*

*of*which many properties are known. ... Here we present new results for

*the*two-point

*degree*correlation function in terms

*of*

*the*clustering coefficient

*of*

*the*

*graphs*for two-dimensional space in particular, with extensions to arbitrary finite ...

*The*Random

*Geometric*

*Graph*(RGG) is a standard spatial network model that plays a role for spatial networks similar to

*the*one played by

*the*Erdös-Rényi random

*graph*for relational ones. ...

##
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Page 143 of Journal of Spacecraft and Rockets Vol. 11, Issue 3
[page]

1974
*
Journal of Spacecraft and Rockets
*

As expected,

*the*torque coefficient changes very rapidly with*the**degree**of*porosity and*the*geo- metry*of**the*disk. ...*Geometrical*pattern*of**the*surface has a very strong effect on C,,. ...##
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Packing plane spanning trees and paths in complete geometric graphs

2017
*
Information Processing Letters
*

We consider

doi:10.1016/j.ipl.2017.04.006
fatcat:exmfvf6aeng6lkhmupn27qwxvy
*the*following question: How many edge-disjoint plane spanning trees are contained in a complete*geometric**graph*GK_n on any set S*of*n points in general position in*the*plane? ... Further, we consider variants*of*this problem by bounding*the*diameter and*the**degree**of**the*trees (in particular considering spanning paths). ... A concept between*graph*-theoretical*thickness*and book*thickness*was later developed by Dillencourt, Eppstein, and Hirschberg [10] : given an abstract*graph*G,*the**geometric**thickness**of*G is*the*smallest ...##
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COMPARATIVE ANALYSIS OF AN IMPELLER GEOMETRY AT DIFFERENT HEADS OF A PUMP

2018
*
Theoretical & Applied Science
*

Calculations

doi:10.15863/tas.2018.12.68.27
fatcat:bg7iuscogvfz7awy2hv4se5cva
*of**the*impellers geometry were carried out at volume fluid flow rate (water)*of*300 m 3 /h. Profiles and*geometric*dimensions*of**the*impeller blades are obtained in*the*spans: 0 and 1. ... It is determined that*the*radial impellers are recommended to be used at*the*pump head*of*20 -25 m.*The*most stable characteristic*of**the*pump operation is observed in this range*of*heads. ...*The*ratio*of**thickness*to*the*tip diameter equal to 0.03 indicates about a*low*probability*of*blockage to fluid flow. ...##
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Geometric Biplane Graphs I: Maximal Graphs

2015
*
Graphs and Combinatorics
*

We study biplane

doi:10.1007/s00373-015-1546-1
fatcat:pitfyvraizenjbkijjiotsmosm
*graphs*drawn on a finite planar point set S in general position. This is*the*family*of**geometric**graphs*whose vertex set is S and can be decomposed into two plane*graphs*. ... We also study extremal properties*of*maximal biplane*graphs*such as*the*maximum number*of*edges and*the*largest maximum connectivity over n-element point sets. ... Note that*the*above generalization*of*plane*graphs*is reminiscent to, although more restrictive than,*the*notion*of**thickness*,*geometric**thickness*, and book*thickness*, which are defined for abstract*graphs*...##
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Anatomy of triply-periodic network assemblies: characterizing skeletal and inter-domain surface geometry of block copolymer gyroids

2018
*
Soft Matter
*

This work was supported by

doi:10.1039/c8sm00078f
pmid:29683466
fatcat:osd2m3nu6rfljlvq3ss6uhevee
*the*U.S. ... ACKNOWLEDGEMENTS*The*authors are grateful to R. Spontak for initial discussions regarding EMT reconstructions*of*triblock networks and R. Kusner for useful discussions regarding TPMS. ... Beyond*the*analysis*of*domain*thickness*, we demonstrate that this simple numerical approximation*of**the*1D skeletal*graph*allows for*the*quantitative characterization*of*other key*geometrical*properties ...##
###
Numerical Research on the Effect of Impactor Shape and Core Characteristics on the Ballistic Impact Response of Marine Sandwich Composite Plates

2019
*
International journal of recent technology and engineering
*

*The*kinetic energy loss

*of*

*the*projectile during

*the*impact is

*the*criteria used to compare

*the*different types

*of*impactors. ...

*The*dynamic response

*of*composite plates to impactors

*of*different shapes is investigated. ...

*The*core material is normally

*low*strength material, but its higher

*thickness*provides

*the*sandwich composite with high bending stiffness with overall

*low*density. ...

##
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A Raster-to-Vector Conversion Concept Based on Industrial Requirements

1988
*
IAPR International Workshop on Machine Vision Applications
*

During this process

dblp:conf/mva/Espelid88
fatcat:t3cx5bvczreo5ibjitgpiwl5wq
*the**geometric*features are extracted from image contour lines. ... With IGES as*the*starting point, covering*the*CAD area, I discuss a number*of*such needs. A strategy for*the*design*of*a r-t-v system that matches*the*requirements listed is then proposed. ... They produces nodes*of**degree*three, they have a free end or merge into another artifact (*the*Xeffect), and their length is proportional to*the*local line*thickness*. ...##
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Finding the Optimal Condition of Exterior Spray Coating for Cookware Products

2015
*
MATEC Web of Conferences
*

From

doi:10.1051/matecconf/20152603012
fatcat:myfpwpxpfjhv5ejndf7y5fbsia
*the*analysis*of**the*experiment, it can be concluded that 23 cm*of*height, 95*degrees**of*gun angle, 5.4 bar*of*air pressure 1.95 seconds*of*spray time, 295*degrees**of*nozzle size is proposed. ... One is studied using an experimental design process, and*the*other is*the**geometric*modeling for*the*process*of*exterior spray coating. ...*The**graph*shown*the*co-responding influence*of*factors affected on*the*volume*of*dry film*thickness*This*graph*showed*the*co-responding influence*of*factors that affected on*the*dry film*thickness*. ...##
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Anatomy of triply-periodic network assemblies: Characterizing skeletal and inter-domain surface geometry of block copolymer gyroids
[article]

2018
*
arXiv
*
pre-print

heterogeneous packing

arXiv:1801.03141v1
fatcat:qazz2uauffcwvpjwfnrcfn5m24
*of*molecular constituents that form*the*networks. ... While TPNs are, in reality, volume-filling patterns*of*spatially-varying molecular composition, physical and structural models most often reduce their structure to lower-dimensional*geometric*objects: ... This work was supported by*the*U.S. ...##
###
The large-scale geometry of right-angled Coxeter groups
[article]

2018
*
arXiv
*
pre-print

This is a survey

arXiv:1807.08787v1
fatcat:xnss5m6uurbehfod7z2m4777da
*of*some aspects*of**the*large-scale geometry*of*right-angled Coxeter groups. ...*The*emphasis is on recent results on their negative curvature properties, boundaries, and their quasi-isometry and commensurability classification. ...*The*notion*of**thickness*was introduced in [BDM09] as a*geometric*obstruction to relative hyperbolicity. An idea*of**the*definitions*of**thickness*and strong algebraic*thickness*is given in Section 5.2. ...
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