Description
The next lecture in the Extremal seminar will be on November 20 at 12:30 in the Nagyterem of the Rényi Institute.
Abstract: Given a family of graphs $\mathcal{F}$, a graph is called $\mathcal{F}$-free if it does not contain any member of $\mathcal{F}$ as a subgraph. The Turán number $ex(n,\mathcal{F})$ of $\mathcal{F}$ is the maximum number of edges in an $n$-vertex $\mathcal{F}$-free graph. The study of Turán number of graphs is a central topic in extremal graph theory. Alon and Frankl, and Gerbner initiated the study of the maximum number of edges in $n$-vertex $F$-free graphs with bounded matching number, i.e., they determined the value of $ex(n,\{F,M_{s+1}\})$, respectively. Given a collection of graphs $(G_1,\ldots,G_t)$ on the same vertex set $V$ of size $n$, a rainbow graph on $V$ is obtained by taking at most one edge from each $G_i$. We say that a collection is rainbow $\mathcal{F}$-free if it contains no rainbow copy of any member of $\mathcal{F}$. In this paper, motivated by the above results, we study three types of rainbow Turán number of $\{F,M_{s+1}\}$ for a given $F$.
Zoom:
Meeting ID: 833 1758 0018
Invite Link: https://us06web.zoom.us/j/83317580018?pwd=1lh6qG2Kwg93dm6G0nb8wAxIlRUEjF.1
Passcode: 364380