Description
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.
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