𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Constructions of covering triangulations with folds

✍ Scribed by André Bouchet

Publisher
John Wiley and Sons
Year
1982
Tongue
English
Weight
704 KB
Volume
6
Category
Article
ISSN
0364-9024

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

Let G be a graph with a known triangular embedding in a surface S, and consider G~(m)~, the composition of G with an independant set of order m. The purpose of this paper is to construct a triangular embedding of G~(m)~ into a surface magnified image by using a covering triangulation with folds. We make the construction for three cases. One of them is used for proving that G~(m)~ can be triangularly embedded into a surface magnified image if G is an Eulerian graph which can be triangularly embedded into a surface S with the same orientability characteristic as magnified image.

📜 SIMILAR VOLUMES

On covering bridged plane triangulations
On covering bridged plane triangulations with balls
✍ Victor Chepoi; Yann Vaxès 📂 Article 📅 2003 🏛 John Wiley and Sons 🌐 English ⚖ 155 KB

## Abstract We show that every plane graph of diameter 2__r__ in which all inner faces are triangles and all inner vertices have degree larger than 5 can be covered with two balls of radius __r__. © 2003 Wiley Periodicals, Inc. J Graph Theory 44: 65–80, 2003

(m)-covering of a triangulation
(m)-covering of a triangulation
✍ Dominique Benard; Andre Bouchet; Jean-Luc Fouquet 📂 Article 📅 1986 🏛 Elsevier Science 🌐 English ⚖ 631 KB

Let G be a graph triangularly imbedded into a surface S, G0,,) is the graph constructed from G by replacing each vertex x by m vertices (x, 0), (x, 1) ..... (x, m-1) and joining two vertices (x, i) and (y, j) by an edge if and only if x and y are joined in G. The main result is that the construction

Group construction of covering arrays
Group construction of covering arrays
✍ Karen Meagher; Brett Stevens 📂 Article 📅 2004 🏛 John Wiley and Sons 🌐 English ⚖ 112 KB

## Abstract A covering array __t__‐__CA__ (__n__, __k__, __g__) is a __k__ × __n__ array on a set of __g__ symbols with the property that in each __t__ × __n__ subarray, every __t__ × 1 column appears at least once. This paper improves many of the best known upper bounds on __n__ for covering array

Asymptotic Number of Triangulations with
Asymptotic Number of Triangulations with Vertices inZ2
✍ S.Yu Orevkov 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 84 KB

Let T 2 n be the set of all triangulations of the square [0, n] 2 with all the vertices belonging to Z 2 . We show that Cn 2 <log Card T 2 n <Dn 2 . ## 1999 Academic Press Triangulations with integral vertices appear in the algebraic geometry. They are used in Viro's method of construction of real

A construction of covers of arithmetic s
A construction of covers of arithmetic schemes
✍ Götz Wiesend 📂 Article 📅 2006 🏛 Elsevier Science 🌐 English ⚖ 175 KB

Let X be a regular arithmetic scheme, i.e. a regular integral separated scheme flat and of finite type over Spec Z. Assume that for all closed irreducible subschemes C ⊆ X of dimension 1 with normalisation C there are given open normal subgroups N C of π 1 ( C), which fulfil the following compatibil