Leírás
Joint work with Cory Palmer
Abstract:
Fix a $k$-chromatic graph $F$. We consider the question to determine for which graphs $H$ does the Tur\'an graph $T_{k-1}(n)$ have the maximum number of copies of $H$ among all $n$-vertex $F$-free graphs (for $n$ large enough). We say that such a graph $H$ is {\it $F$-Tur\'an-good}. In addition to some general results, we give (among others) the following concrete results:
\begin{enumerate}
\item[(i)] For every complete multipartite graph $H$, there is $k$ large enough such that $H$ is $K_k$-Tur\'an-good.
\item[(ii)] The path $P_3$ is $F$-Tur\'an-good for $F$ with $\chi(F) \geq 4$.
\item[(iii)] The path $P_4$ and cycle $C_4$ are $C_5$-Tur\'an-good.
\item[(iv)] The cycle $C_4$ is $F_2$-Tur\'an-good where $F_2$ is the graph of two triangles sharing exactly one vertex.
\end{enumerate}
Zoom link:
https://zoom.us/j/2961946869