Leírás
Véges Geom Szeminárium:
Abstract: We prove an asymptotic result on the maximum number of $k$-vertex subtrees in binary trees of given order. This problem turns out to be equivalent to determine the maximum number of $k+2$-cycles in $n$-vertex outerplanar graphs, thus we settle the generalized outerplanar Turán number for all cycles.\\
We also determine the exponential growth of the generalized outerplanar Turán number of paths $P_k$ as a function of $k$ which implies the order of magnitude of the generalized outerplanar Turán number of arbitrary trees.
The bounds are strongly related to the sequence of Catalan numbers.
Zoom link és jelszó - köszönet érte Somlai Gábornak! :
https://zoom.us/j/91259930748?pwd=cjRUakdwN1cvMzZ6aWNoaG53TkdyUT09
Meeting ID: 912 5993 0748
Passcode: 443160