Walks through every edge exactly twice II

Abstract

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. © 1996 John Wiley & Sons, Inc.