Circuit Covers of Signed Eulerian Graphs

TL;DR

This paper proves that signed Eulerian graphs with no coloops in their signed-graphic matroid have a circuit cover of at most six circuits, confirming a conjecture in this specific case.

Contribution

It establishes the conjecture for signed Eulerian graphs, advancing understanding of circuit covers in signed graphs.

Findings

Proves the conjecture for signed Eulerian graphs.

Shows existence of a 6-cover for these graphs.

Enhances knowledge of signed graph circuit covers.

Abstract

A signed circuit cover of a signed graph is a natural analog of a circuit cover of a graph, and is equivalent to a covering of its corresponding signed-graphic matroid with circuits. It was conjectured that a signed graph whose signed-graphic matroid has no coloops has a 6-cover. In this paper, we prove that the conjecture holds for signed Eulerian graphs.