Leírás
Gerbner Dániel: Generalized rainbow Turán problems
joint work with Tamás Mészáros, Abhishek Methuku and Cory Palmer
abstract:
Alon and Shikhelman initiated the systematic study of the following generalized Turán problem: for fixed graphs $H$ and $F$ and an integer $n$, what is the maximum number of copies of $H$, that can appear in an $n$-vertex $F$-free graph?
An edge-colored graph is called rainbow if all its edges have different colors. The rainbow Turán number of $F$ is defined as the maximum number of edges in a graph on $n$ vertices that has a proper edge-coloring with no rainbow copy of $F$. The study of rainbow Turán problems was initiated by Keevash, Mubayi, Sudakov and Verstra\"ete.
In this paper, we study the following natural generalization of these two problems: What is the maximum number of copies of $H$ in an $n$-vertex graph that has a proper edge-coloring without a rainbow copy of $F$? We focus on the case $H=F$ and establish new results for paths, cycles, trees and forests.