Department of
Applied
Mathematics

Vertex-minors and pivot-minors of graphs

Sang-il Oum

Kaist - Korea Advanced Institute of Science and Technology

Abstract

We will survey vertex- and pivot-minor relations of graphs which are defined in terms of local complementation and pivot operations, respectively, on graphs. Many theorems on graph minors can be extended to graph vertex- or pivot-minors. We will discuss various known aspects and then talk about partial results towards some conjectures generalizing some of the deepest theorems in structural graph theory including the graph minor theorem of Robertson and Seymour. No previous background on the graph theory is necessary for this talk.