From the basics of extremal graph theory to bipartite Turan numbers of trees and star forests (Omid Khormali, HMC)

Extremal graph theory asks how many edges a graph can have while avoiding a given substructure. We will begin with a brief, accessible introduction to this area, before turning to a natural variant, the bipartite Turan number $(m,n;H)$, which restricts the host graph to be bipartite. This setting is especially natural when $H$ itself is bipartite, such as a tree or star forest. We present new results determining the leading-order bipartite Turan number for trees and the exact bipartite Turan number for star forests, along with a sketch of the key proof ideas.