Large triangle-free subgraphs in graphs withoutK 4

1986 ◽  
Vol 2 (1) ◽  
pp. 135-144 ◽  
Author(s):  
P. Frankl ◽  
V. Rödl
Keyword(s):  
Large Triangle

scholarly journals Impact of Different Components and Boundary Conditions on the Eigenfrequencies of a Magnet–Girder Assembly

Instruments ◽  
2021 ◽  
Vol 5 (3) ◽  
pp. 29
Author(s):  
Simone Andresen
Keyword(s):  
Boundary Conditions ◽  
Particle Beam ◽  
Design Development ◽  
Material Density ◽  
Electron Synchrotron ◽  
Support Points ◽  
Beam Stability ◽  
Development Processes ◽  
Large Triangle ◽  
The Impact

Synchrotron radiation facilities are very important in different areas of fundamental and applied science to investigate structures or processes at small scales. Magnet–girder assemblies play a key role for the performance of such accelerator machines. High structural eigenfrequencies of the magnet–girder assemblies are required to assure a sufficient particle beam stability. The objective of the present parametric study was to numerically investigate and quantify the impact of different boundary conditions and components on the magnet–girder eigenfrequencies. As case studies, two 3 m long girder designs following the specifications of the PETRA IV project at DESY (German Electron Synchrotron, Hamburg, Germany) were selected. High magnet–girder assembly eigenfrequencies were achieved by, e.g., positioning the magnets close to the upper girder surface, increasing the connection stiffness between the magnets and the girder and between the girder and the bases, and positioning the girder support points as high as possible in the shape of a large triangle. Comparing the E/ρ ratio (E: Young’s modulus, ρ: material density) of different materials was used as a first approach to evaluate different materials for application to the girder. Based on the findings, general principles are recommended to be considered in the future girder design development processes.

Out-of-Core Progressive Lossless Compression and Selective Decompression of Large Triangle Meshes

2009 ◽  
Author(s):  
Zhiyan Du ◽  
Pavel Jaromersky ◽  
Yi-Jen Chiang ◽  
Nasir Memon
Keyword(s):  
Lossless Compression ◽  
Triangle Meshes ◽  
Large Triangle

scholarly journals Large triangle packings and Tuza’s conjecture in sparse random graphs

2020 ◽  
Vol 29 (5) ◽  
pp. 757-779 ◽  
Author(s):  
Patrick Bennett ◽  
Andrzej Dudek ◽  
Shira Zerbib
Keyword(s):  
Greedy Algorithm ◽  
Random Graph ◽  
Random Graphs ◽  
Maximum Size ◽  
Packing Number ◽  
Edge Disjoint ◽  
Large Triangle

AbstractThe triangle packing number v(G) of a graph G is the maximum size of a set of edge-disjoint triangles in G. Tuza conjectured that in any graph G there exists a set of at most 2v(G) edges intersecting every triangle in G. We show that Tuza’s conjecture holds in the random graph G = G(n, m), when m ⩽ 0.2403n3/2 or m ⩾ 2.1243n3/2. This is done by analysing a greedy algorithm for finding large triangle packings in random graphs.

Kinetic Occlusion by Apparent Movement

Perception ◽  
1985 ◽  
Vol 14 (2) ◽  
pp. 145-149 ◽  
Author(s):  
Stuart M Anstis ◽  
Vilayanur S Ramachandran
Keyword(s):  
Visual System ◽  
Apparent Movement ◽  
Large Triangle

A small square and a large triangle below it were presented in the first frame. These were switched off and replaced by a triangle alone in the second frame, shifted horizontally and upwards. The triangle appeared to move obliquely, as expected, but most observers also saw the square moving horizontally and hiding behind the triangle, although there was no stimulus corresponding to it in the second frame. The visual system invokes the occlusion ‘hypothesis’ in order to explain the otherwise mysterious disappearance of the square. The experiment suggests that apparently intelligent solutions can be rapidly computed by the visual system.

Intersection Patterns of Families of Convex Sets

1982 ◽  
Vol 34 (4) ◽  
pp. 921-931
Author(s):  
M. Katchalski ◽  
A. Liu
Keyword(s):  
General Position ◽  
Convex Sets ◽  
Large Triangle

In this paper, we study the intersection pattern of families of convex sets. Since we only consider finite families, we may assume that the sets are also compact.As an example, we consider families of 5 convex sets in R2 such that every two intersect and no three intersect. One such family that comes immediately to mind is that of 5 lines in general position. However, this is not the only family which exhibits this intersection pattern. Fig. 1 shows a family of 3 lines (sides of the large triangle) and 2 triangles (inscribed in the large triangle) that has this property.

scholarly journals Graphs without large triangle free subgraphs

1991 ◽  
Vol 87 (2) ◽  
pp. 119-131 ◽  
Author(s):  
B. Bollobás ◽  
H.R. Hind
Keyword(s):  
Large Triangle

scholarly journals Dense Graphs With a Large Triangle Cover Have a Large Triangle Packing

2012 ◽  
Vol 21 (6) ◽  
pp. 952-962 ◽  
Author(s):  
RAPHAEL YUSTER
Keyword(s):  
Absolute Constant ◽  
The Other ◽  
Asymptotically Optimal ◽  
Edge Disjoint ◽  
Other Hand ◽  
Dense Graphs ◽  
Large Triangle ◽  
Odd Cycles ◽  
Asymptotic Validity

It is well known that a graph with m edges can be made triangle-free by removing (slightly less than) m/2 edges. On the other hand, there are many classes of graphs which are hard to make triangle-free, in the sense that it is necessary to remove roughly m/2 edges in order to eliminate all triangles.We prove that dense graphs that are hard to make triangle-free have a large packing of pairwise edge-disjoint triangles. In particular, they have more than m(1/4+cβ) pairwise edge-disjoint triangles where β is the density of the graph and c ≥ is an absolute constant. This improves upon a previous m(1/4−o(1)) bound which follows from the asymptotic validity of Tuza's conjecture for dense graphs. We conjecture that such graphs have an asymptotically optimal triangle packing of size m(1/3−o(1)).We extend our result from triangles to larger cliques and odd cycles.

scholarly journals Robust GPU-based intersection algorithm for a large triangle set

2011 ◽  
Vol 17 (3) ◽  
pp. 9-19 ◽  
Author(s):  
경민호 ◽  
JUNG-JU CHOI ◽  
곽종근
Keyword(s):  
Intersection Algorithm ◽  
Large Triangle

scholarly journals Triangle Free Sets and Arithmetic Progressions – Two Pisier Type Problems

10.37236/1639 ◽  
2002 ◽  
Vol 9 (1) ◽  
Author(s):  
Dennis Davenport ◽  
Neil Hindman ◽  
Dona Strauss
Keyword(s):  
Finite Subset ◽  
Arithmetic Progressions ◽  
Large Triangle ◽  
Free Subset ◽  
Free Sets

Let ${\cal P}_f({\bf N})$ be the set of finite nonempty subsets of ${\bf N}$ and for $F,G\in{\cal P}_f({\bf N})$ write $F < G$ when $\max F < \min G$. Let $X=\{(F,G):F,G\in{\cal P}_f({\bf N})$ and $F < G\}$. A triangle in $X$ is a set of the form $\{(F\cup H,G),(F,G),(F,H\cup G)\}$ where $F < H < G$. Motivated by a question of Erdős, Nešetríl, and Rödl regarding three term arithmetic progressions, we show that any finite subset $Y$ of $X$ contains a relatively large triangle free subset. Exact values are obtained for the largest triangle free sets which can be guaranteed to exist in any set $Y\subseteq X$ with $n$ elements for all $n\leq 14$.

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