A note on shortest circuit cover of 3-edge colorable cubic signed graphs

A {sign-circuit cover} $\mathcal{F}$ 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 M'a$\check{\text{c}}$ajov'a, Raspaud, Rollov'a, and \v{S}koviera (JGT 2016) and received many attentions in recent years. In this paper, we show that every flow-admissible 3-edge colorable cubic signed graph $(G,\sigma )$ has a sign-circuit cover with length at most $\frac{20}{9}\mathrm{\mid }E(G)\mathrm{\mid }$.