# Shorter signed circuit covers of graphs

## TL;DR

This paper improves the upper bound on the total length of signed circuit covers in flow-admissible signed graphs, demonstrating more efficient coverings than previously known, through new results on trees of Eulerian graphs.

## Contribution

It introduces a tighter bound for signed circuit covers in flow-admissible graphs and develops new methods involving trees of Eulerian graphs.

## Key findings

- Signed circuit covers can be bounded by (3+2/3) times the number of edges.
- New results on signed circuit covers of trees of Eulerian graphs.
- Improved upper bounds compared to previous work.

## Abstract

A signed circuit is a minimal signed graph (with respect to inclusion) that admits a nowhere-zero flow. We show that each flow-admissible signed graph on $m$ edges can be covered by signed circuits of total length at most $(3+2/3)\cdot m$, improving a recent result of Cheng et al. [manuscript, 2015]. To obtain this improvement we prove several results on signed circuit covers of trees of Eulerian graphs, which are connected signed graphs such that removing all bridges results in a collection of Eulerian graphs.