✦ LIBER ✦

Diameter-preserving orientations of the torus

✍ Scribed by Konig, Jean-Claude; Krumme, David W.; Lazard, Emmanuel

Publisher: John Wiley and Sons
Year: 1998
Tongue: English
Weight: 138 KB
Volume: 32
Category: Article
ISSN: 0028-3045
DOI: 10.1002/(sici)1097-0037(199808)32:1<1::aid-net1>3.0.co;2-g

No coin nor oath required. For personal study only.

✦ Synopsis

The diameter of a directed graph is the maximum of the lengths of the shortest paths between all pairs of vertices. A directed graph is said to be tightly oriented if it has the same diameter as its undirected image graph. Our main result is tight orientations for all sufficiently large toroids, except those whose sizes in both dimensions are odd. We also prove the impossibility of tightly orienting all the toroids for which we do not present tight orientations, and we give partial results for dimensionality higher than two.

📜 SIMILAR VOLUMES

Complexity of approximating the oriented

Complexity of approximating the oriented diameter of chordal graphs

✍ Fedor V. Fomin; Martín Matamala; Ivan Rapaport 📂 Article 📅 2004 🏛 John Wiley and Sons 🌐 English ⚖ 135 KB

## Abstract The oriented diameter of a bridgeless connected undirected (__bcu__) graph __G__ is the smallest diameter among all the diameters of strongly connected orientations of __G__. We study algorithmic aspects of determining the oriented diameter of a chordal graph. We (a) construct a linear‐

Integrability for the Jacobian of Orient

Integrability for the Jacobian of Orientation Preserving Mappings

✍ H. Brezis; N. Fusco; C. Sbordone 📂 Article 📅 1993 🏛 Elsevier Science 🌐 English ⚖ 157 KB

Re-envisioning the training and practice

Re-envisioning the training and practice of clinical psychologists: Preserving science and research orientations in the face of change

✍ Joan M. Cook; James C. Coyne 📂 Article 📅 2005 🏛 John Wiley and Sons 🌐 English ⚖ 61 KB 👁 1 views

## Abstract We argue for preservation of an expectation of psychologists that approach human problems from an evidence‐based perspective. Acquisition of the requisite knowledge, skills, and practical experience require access to resources outside of graduate psychology programs. Whether adhering to

Irreducible Quadrangulations of the Toru

Irreducible Quadrangulations of the Torus

✍ Atsuhiro Nakamoto 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 423 KB

On some minimal graphs of the torus

✍ R. Bodendiek; K. Wagner 📂 Article 📅 1985 🏛 John Wiley and Sons 🌐 English ⚖ 259 KB 👁 1 views

## Let be the set of finite, simple and nondirected graphs being not embeddable into the torus. Furthermore let >4 be a partial order-relation and M, (r) the minimal basis of I'. In this paper we determine three graphs of M, (r) being embeddable into the projective plane and containing the subgrap

Grid Minors of Graphs on the Torus

✍ M. Degraaf; A. Schrijver 📂 Article 📅 1994 🏛 Elsevier Science 🌐 English ⚖ 197 KB