✦ LIBER ✦

Walks through every edge exactly twice II

✍ Scribed by Keir, Jennifer; Richter, Bruce

Publisher: John Wiley and Sons
Year: 1996
Tongue: English
Weight: 603 KB
Volume: 21
Category: Article
ISSN: 0364-9024
DOI: 10.1002/(sici)1097-0118(199603)21:3<301::aid-jgt4>3.0.co;2-u

No coin nor oath required. For personal study only.

✦ Synopsis

In this paper we develop a theory of sets of walks traversing every edge twice. Archdeacon, Bonnington, and Little proved that a graph G is planar if and only if there is a set of closed walks w in G traversing every edge exactly twice such that several sets of edges derived from -W are all cocycles. One consequence of the current work is a simple proof of the ABL theorem.

📜 SIMILAR VOLUMES

Walks through every edge exactly twice

✍ R. Bruce Richter 📂 Article 📅 1994 🏛 John Wiley and Sons 🌐 English ⚖ 268 KB

## Abstract In this article, we develop a theory of walks traversing every edge exactly twice. Rosenstiehl and Read proved that if __G__ is a graph with no set of edges that is simultaneously a cycle and a cocycle, then __G__ is planar if and only if there is a closed walk __W__ in __G__ traversing