Negative closed walks in signed graphs: A note

TL;DR

This paper revises the characterization of negative closed walks in signed graphs, correcting a previous claim and providing a new, valid characterization to better understand the structure of signed graphs.

Contribution

The authors identify flaws in the existing characterization of negative closed walks and propose a new, accurate characterization for signed graphs.

Findings

Previous characterization was invalid

New characterization accurately describes negative closed walks

Clarifies the structure of signed graphs with negative walks

Abstract

Recently Naserasr, Sopena, and Zaslavsky [R. Naserasr, \'E. Sopena, T. Zaslavsky,Homomorphisms of signed graphs: An update, arXiv: 1909.05982v1 [math.CO] 12 Sep 2019.] published a report on closed walks in signed graphs. They gave a characterization of the sets of closed walks in a graph $G$ which corespond to the set of negative walks in some signed graph on $G$. In this note we show that their characterization is not valid and give a new characterization.