Displaying blocking pairs in signed graphs

A signed graph is a pair (G,Σ) where G is a graph and Σ is a set of edges of G. A cycle of G is balanced if it contains an even number of edges of Σ, and unbalanced otherwise. A blocking pair of (G,Σ) is a pair of vertices {s,t} such that every unbalanced cycle intersects at least one of s or t. In this paper, we characterize when the blocking pairs of a signed graph can be represented by 2-cuts in an auxiliary graph. We discuss the relevance of this result to the problem of recognizing even cycle matroids and to the problem of characterizing signed graphs with no −K5 minor.