Liu, Xizhi: A Short Story on the Graph Inducibility Problem

The inducibility problem, introduced by Pippenger and Golumbic in 1975, asks for the maximum number of induced copies of a graph $F$ in an $n$-vertex graph. Despite decades of research, determining the inducibility of a given graph $F$ remains highly challenging; the four-vertex path serves as a notable example. In this talk, we focus on the case where $F$ is a complete multipartite graph (a case that still remains open in general) and survey some recent progress on this topic.