A note on shortest sign-circuit cover of signed 3-edge-colorable cubic graphs (Q2168862)

A sign-circuit cover \(F\) of a signed graph (G; \(\sigma\)) is a family of sign-circuits which covers all edges of (G; \(\sigma\)). The shortest sign-circuit cover problem was initiated by \textit{E. Máčajová} et al. [J. Graph Theory 81, No. 2, 120--133 (2016; Zbl 1332.05066)] and received much attention in recent years. A well-known conjecture, the shortest cycle cover conjecture, was proposed by \textit{N. Alon} and \textit{M. Tarsi} [SIAM J. Algebraic Discrete Methods 6, 345--350 (1985; Zbl 0581.05046)]. Here, the authors show that every flow-admissible signed 3-edgecolorable cubic graph (G; \(\sigma\)) has a sign-circuit cover with length at most \(\frac{20}{9}|E(G)|\). The authors pose the problem to determine the optimal upper bound for the shortest sign-circuit cover of a signed 3-edge-colorable cubic graph that remains open. This paper has many interesting results and many future problems are posed. This will help many young researchers working in the area of signed graphs. I have advised younger researchers to read this paper.