Speaker: Dong Ye

Title: On circuit covers of signed graphs
 
 Abstract: A signed graph (G, σ) is a graph G associated with a mapping σ: E(G) -> {-1,+1}. A circuit of a signed graph (G, σ)  is a minimal dependent set of signed graphical matroid of (G, σ). More specifically, a circuit is either a balanced cycle or a barbell consisting of two unbalanced cycles joined by a path.  Bouchet proved that a signed graph (G, σ) has a circuit cover if and only if it admits a nonwhere zero integer flow. In this talk, we are going to survey recent developments related to circuit covers of signed graphs.