Shorter signed circuit covers of graphs

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 )0.15em ⋅0.15em m, improving a recent result of Cheng et al. 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.