Given a graph , we define to be the minimum value of for which there exists a constant such that every -connected graph with at least vertices contains as a minor. The value of is known to be tied to the vertex cover number , and in fact $\tau(G)\leq …
Let and be graphs. The subgraph counting function is defined as the maximum possible number of subgraphs in an -vertex -free graph. This function is a direct generalization of the Turán function as . The systematic study of was initiated by Alon and Shikhelman in 2016 who generalized several classical …
Given a graph , there are several natural hypergraph families one can define. Among the least restrictive is the family of so-called Berge copies of the graph . In this talk, we discuss Turán problems for families in -uniform hypergraphs for various graphs . In particular, we are interested in general results in …