Description
Abstract:
We consider a natural generalisation of Turán’s forbidden subgraph problem and the Ruzsa-Szemerédi (6, 3) problem.
Let ex_F (n, G) denote the maximum number of edge-disjoint copies of a fixed graph F that can be placed on an
n-vertex ground set without forming a subgraph G, whose edges are from different F-copies. One can also think of this
as placing graphs F of distinct colors and want to avoid a multicolor G.
First we discuss several related old results that fit into this framework.
Then we characterize those pairs (F, G) for which the order of magnitude of ex_F (n, G) is quadratic as a generalisation
of the Erdős-Stone-Simonovits theorem.
We continue with proving several asymptotic results using various tools from the Szemeredi regularity lemma
and supersaturation to graph packing results and additive number theory. Finally we show some applications.
Joint work with András Imolay, Benedek Kovács, Benedek Váli and János Karl
The lecture can be followed by zoom:
https://us06web.zoom.us/j/81239725712?pwd=eDlXNXR1cUhVbWRNbUdEc1dEcWo2dz09
If it is needed, the passcode is 670457.