Flows and Circuit Covers in Signed Graphs

 A signed graph G is a graph associated with a mapping
σ: E( G) →{+1, −1}. Signed graphs can be used to present surface duals of digraphs embedded in non-orientable surfaces. A signed graph is coverable if each edge is contained in some signed circuit. The edges of a signed circuit in a signed graph corresponds a minimal dependent set in the signed graphic matroid. An oriented signed graph (bidirected graph) has a nowhere-zero integer flow if and only if it is coverable. A signed circuit cover of G is a collection of signed circuits which covers all the edges of G. Signed circuit covers is a new topic drawing attention in recent years. In this talk, we give a brief survey of known results and open problems on signed circuit covers of signed graphs.