Walks through every edge exactly twice
R. Bruce Richter · Journal of Graph Theory · 1994
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 every edge exactly twice such that certain sets of edges derived from W are all cocycles. One consequence of the current work is a simple proof of the Rosenstiehl‐Read theorem. Another is an unusual method for determining the rank (over the integers modulo 2) of a symmetric matrix obtained from a circle graph.