Concept

Planar separator theorem

Related publications (65)

Non-planarity of Markoff graphs mod p

We prove the non-planarity of a family of 3-regular graphs constructed from the solutions to the Markoff equation x2 + y2 + z2 = xyz modulo prime numbers greater than 7. The proof uses Euler characteristic and an enumeration of the short cycles in these gr ...

Berlin2024

Pre-annealing for improved LPCVD deposited boron-doped poly-Si hole-selective contacts

Franz-Josef Haug, Luca Massimiliano Antognini, Josua Andreas Stückelberger, Xinyu Zhang, Zhao Wang, Jie Yang

We demonstrate the beneficial effect of a pre-annealing step prior to the boron diffusion on passivation and contact resistivity of industrially LPCVD deposited poly-Si/SiOX hole-selective contacts. We investigate the influence of the pre-annealing tempera ...

ELSEVIER2023

A Solution to Adaptive Mobile Manipulator Throwing

Aude Billard, Yang Liu, Aradhana Nayak

Mobile manipulator throwing is a promising method to increase the flexibility and efficiency of dynamic manipulation in factories. Its major challenge is to efficiently plan a feasible throw under a wide set of task specifications. We show that the mobile ...

IEEE2022

3D Buoyancy-Driven Propagation of Hydraulic Fractures and their Applications to Magmatic Plumbing Systems

Brice Tanguy Alphonse Lecampion, Andreas Möri

Understanding how dykes behave as they propagate through the Earth’s crust has been a hot topic for VIPS researchers for many years–to see how magmatic intrusion models have evolved over the past century check out Tim Davis’ blog post! Through numerically ...

2022

Atomic subgraphs and the statistical mechanics of networks

Sofia Charlotta Olhede

We develop random graph models where graphs are generated by connecting not only pairs of vertices by edges, but also larger subsets of vertices by copies of small atomic subgraphs of arbitrary topology. This allows for the generation of graphs with extens ...

2021

Minimal graphs for 2-factor extension

Dominique de Werra

Let G = (V, E) be a simple loopless finite undirected graph. We say that G is (2-factor) expandable if for any non-edge uv, G + uv has a 2-factor F that contains uv. We are interested in the following: Given a positive integer n = vertical bar V vertical b ...

ELSEVIER2020

Realizability of planar point embeddings from angle measurements

Majed El Helou, Adam James Scholefield, Frederike Dümbgen

Localization of a set of nodes is an important and a thoroughly researched problem in robotics and sensor networks. This paper is concerned with the theory of localization from inner-angle measurements. We focus on the challenging case where no anchor loca ...

2020

Fast and Space Efficient Spectral Sparsification in Dynamic Streams

Mikhail Kapralov, Jakab Tardos, Navid Nouri, Aidasadat Mousavifar

In this paper, we resolve the complexity problem of spectral graph sparcification in dynamic streams up to polylogarithmic factors. Using a linear sketch we design a streaming algorithm that uses (O) over tilde (n) space, and with high probability, recover ...

ASSOC COMPUTING MACHINERY2020

Planar Point Sets Determine Many Pairwise Crossing Segments

János Pach, Gábor Tardos

We show that any set of n points in general position in the plane determines n(1-o(1)) pairwise crossing segments. The best previously known lower bound, Omega(root n), was proved more than 25 years ago by Aronov, Erdos, Goddard, Kreitman, Krugerman, Pach, ...

ASSOC COMPUTING MACHINERY2019

Vector-Based 3D Graphic Statics: a framework for the design of spatial structures based on the relation between form and forces

Corentin Jean Dominique Fivet, Pierluigi D'Acunto

This article develops a vector-based 3D graphic statics framework that uses synthetic and intuitive graphical means for the analysis and design of spatial structures such as networks of bar elements in static equilibrium. It is intended to support the coll ...

2019

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