Publications related to Vertex arrangement

A Note on Lenses in Arrangements of Pairwise Intersecting Circles in the Plane

Let F be a family of n pairwise intersecting circles in the plane. We show that the number of lenses, that is convex digons, in the arrangement induced by F is at most 2n - 2. This bound is tight. Furthermore, if no two circles in F touch, then the geometr ...

Electronic Journal Of Combinatorics2024

Real-Time Distributed Algorithms for Nonconvex Optimal Power Flow

Colin Neil Jones, Georgios Stathopoulos, Jean-Hubert Hours, Yuejiang Liu

The optimal power flow (OPF) problem, a fundamental problem in power systems, is generally nonconvex and computationally challenging for networks with an increasing number of smart devices and real-time control requirements. In this paper, we first investi ...

2017

On Simplices in Diameter Graphs in R-4

Andrei Kupavskii

A graph G is a diameter graph in R-d if its vertex set is a finite subset in R-d of diameter 1 and edges join pairs of vertices a unit distance apart. It is shown that if a diameter graph G in R-4 contains the complete subgraph K on five vertices, then any ...

Maik Nauka/Interperiodica/Springer2017

Possibility of an unconventional spin state of Ir4+ in Ba21Ir9O43 single crystal

László Forró, Henrik Moodysson Rønnow, Arnaud Magrez, Oleg Yazyev, Alla Arakcheeva, Ivica Zivkovic, Bálint Náfrádi, Lin Yang, Andrea Pisoni, Sergiy Katrych, Jacim Jacimovic, Noore Elahi Shaik

We report the synthesis of single crystals of a novel layered iridate Ba21Ir9O43 and present the crystallographic, transport, and magnetic properties of this material. The compound has a hexagonal structure with two iridium oxide layers stacked along the c ...

Amer Physical Soc2016

Grain Boundaries in Graphene on SiC(000(1)over-bar) Substrate

Oleg Yazyev, Fernando Gargiulo

Grain boundaries in epitaxial graphene on the SiC(000 (1) over bar) substrate are studied using scanning tunneling microscopy and spectroscopy. All investigated small-angle grain boundaries show pronounced out-of-plane buckling induced by the strain fields ...

Amer Chemical Soc2014

In-Plane Fabricated Insulated Gold-Tip Probe For Electrochemical And Molecular Experiments

Nico de Rooij, Terunobu Akiyama, Sebastian Gautsch, Peter Van der Wal, Yexian Wu

In this contribution we present a scanning probe with a gold-tip completely encapsulated with insulator all the way to the apex. The probe fabrication is unique owing to an in-plane arrangement in which the width of the cantilever is defined by deep reacti ...

IEEE2013

New Results in the Theory of Linear and Integer Programming

Nicolai Hähnle

The polynomial Hirsch conjecture states that the vertex-edge diameter of a d-dimensional polyhedron with n facets is bounded by a polynomial in d and n. For the special case where the polyhedron is defined as the set of points satisfying a system Ax ≤ b of ...

EPFL2012

Hanani-Tutte and Monotone Drawings

Radoslav Fulek

A drawing of a graph is x-monotone if every edge intersects every vertical line at most once and every vertical line contains at most one vertex. Pach and Toth showed that if a graph has an x-monotone drawing in which every pair of edges crosses an even nu ...

Springer-Verlag Berlin2011

Conway's conjecture for monotone thrackles

János Pach

A drawing of a graph in the plane is called a thrackle if every pair of edges meet precisely once, either at a common vertex or at a proper crossing. According to Conway's conjecture, every thrackle has at most as many edges as vertices. We prove this conj ...

Mathematical Association of America2011

Adjacent Crossings Do Matter

Radoslav Fulek

In a drawing of a graph, two edges form an odd pair if they cross each other an odd number of times. A pair of edges is independent if they share no endpoint. For a graph G, let ocr(G) be the smallest number of odd pairs in a drawing of G and let iocr(G) b ...

Springer-Verlag Berlin2011

A computational approach to Conway's thrackle conjecture

János Pach, Radoslav Fulek

A drawing of a graph in the plane is called a thrackle if every pair of edges meets precisely once, either at a common vertex or at a proper crossing. Let t(n) denote the maximum number of edges that a thrackle of n vertices can have. According to a 40 yea ...

2011

A Computational Approach to Conway's Thrackle Conjecture

János Pach, Radoslav Fulek

A drawing of a graph in the plane is called a thrackle if every pair of edges meets precisely once, either at a common vertex or at a proper crossing. Let t(n) denote the maximum number of edges that a thrackle of n vertices can have. According to a 40 yea ...

Springer2010