𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Characterizing planarity using theta graphs

✍ Scribed by Archdeacon, Dan; S?r�n?, Josef

Publisher
John Wiley and Sons
Year
1998
Tongue
English
Weight
87 KB
Volume
27
Category
Article
ISSN
0364-9024

No coin nor oath required. For personal study only.

✦ Synopsis

A theta graph is a homeomorph of K 2,3 . In an embedded planar graph the local rotation at one degree-three vertex of a theta graph determines the local rotation at the other degree-three vertex. Using this observation, we give a characterization of planar graphs in terms of balance in an associated signed graph whose vertices are K 1,3 subgraphs and whose edges correspond to theta graphs.

📜 SIMILAR VOLUMES

An algebraic characterization of planar
An algebraic characterization of planar graphs
✍ Dan Archdeacon; C. Paul Bonnington; Charles H. C. Little 📂 Article 📅 1995 🏛 John Wiley and Sons 🌐 English ⚖ 773 KB

## Abstract A cycle in a graph is a set of edges that covers each vertex an even number of times. A cocycle is a collection of edges that intersects each cycle in an even number of edges. A bicycle is a collection of edges that is both a cycle and a cocycle. The cycles, cocycles, and bicycles each

An algebraic characterization of project
An algebraic characterization of projective-planar graphs
✍ Lowell Abrams; Daniel C. Slilaty 📂 Article 📅 2003 🏛 John Wiley and Sons 🌐 English ⚖ 114 KB

## Abstract We give a detailed algebraic characterization of when a graph __G__ can be imbedded in the projective plane. The characterization is in terms of the existence of a dual graph __G__\* on the same edge set as __G__, which satisfies algebraic conditions inspired by homology groups and inte

Characterizing 3-connected planar graphs
Characterizing 3-connected planar graphs and graphic matroids
✍ Manoel Lemos; Talmage James Reid; Haidong Wu 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 98 KB

## Abstract A well‐known result of Tutte states that a 3‐connected graph __G__ is planar if and only if every edge of __G__ is contained in exactly two induced non‐separating circuits. Bixby and Cunningham generalized Tutte's result to binary matroids. We generalize both of these results and give n

Erratum: Graph-theoretic characterizatio
Erratum: Graph-theoretic characterization of the matrix property of full irreducibility without using a transversal
✍ Aram K. Kevorkian 📂 Article 📅 1979 🏛 John Wiley and Sons 🌐 English ⚖ 41 KB

In Lemmas 6 and 11 of the above article, the word proper should be dropped. The condition C?(Uf=, P i ) f @ which appeared in the third line of Lemma 11 should be replaced by C?(Uf=, Pi)nPk+l # gf and the lower bound 2 min ( H A ) which appeared in the fifth line should be replaced by 2 X ( U E 1 P

Hemodynamic characterization of focal he
Hemodynamic characterization of focal hepatic lesions: Role of ferucarbotran-enhanced dynamic MR imaging using T2-weighted multishot spin-echo echo-planar sequence
✍ Masatoshi Hori; Takamichi Murakami; Tonsok Kim; Riccardo Iannaccone; Hisashi Abe 📂 Article 📅 2006 🏛 John Wiley and Sons 🌐 English ⚖ 463 KB

## Abstract ## Purpose To investigate the role of ferucarbotran‐enhanced dynamic MR imaging using multishot spin‐echo echo‐planar sequence in the evaluation of hemodynamics of focal hepatic lesions. ## Materials and Methods Sixty‐three focal hepatic lesions (24 benign and 39 malignant) from 53 c