Generalized Tur\'an Problems
Báo cáo viên: Casey Tompkins. VIASM

Thời gian: 9h30, Thứ 5, ngày 19/12/2019.
Địa điểm: Phòng 612, nhà A6, Viện Toán học, 18 Hoàng Quốc Việt
Tóm tắt: The classical Tur'an extremal problem asks the following: Given a graph $F$, how many edges can an $n$-vertex graph have which does not contain $F$ as a subgraph? In this talk we discuss two recent extensions of this problem and their connections.  One the one hand, Alon and Shikhelman introduced a more general extremal problem wherein rather than edges we maximize the number of copies of some other fixed graph $H$ in an $n$-vertex $F$-free graph. In a different direction, Gerbner and Palmer defined a natural hypergraph version of the Tur'an problem, in which for a given graph $F$, a simple family of hypergraphs generated from $F$ is forbidden.  We discuss the connections between these problems and recent progress in understanding the order of growth of the solutions.  Most of the results discussed will be joint work with Gr'osz and Methuku