Graph theory seminar - Katherine Naismith

Extensions of Signed Graphs

Abstract: 

A signed graph is a pair (G, S), where S is a subset of E(G). We can extend a signed graph by adding edges, or by splitting vertices. We will address two questions about extensions of signed graphs. The first is: How can we minimally extend an embedded signed graphs so as to "break" its embedding? The second question is related: When does an embedded signed graph extend uniquely? These results find application in developing a characterization theorem for signed graphs with no odd-K5 minor.