Many $H$copies in graphs with a forbidden tree
Abstract
For graphs $H$ and $F$, let $\operatorname{ex}(n, H, F)$ be the maximum possible number of copies of $H$ in an $F$free graph on $n$ vertices. The study of this function, which generalises the wellstudied Turán numbers of graphs, was initiated recently by Alon and Shikhelman. We show that if $F$ is a tree then $\operatorname{ex}(n, H, F) = \Theta(n^r)$ for some integer $r = r(H, F)$, thus answering one of their questions.
 Publication:

arXiv eprints
 Pub Date:
 November 2018
 arXiv:
 arXiv:1811.04287
 Bibcode:
 2018arXiv181104287L
 Keywords:

 Mathematics  Combinatorics;
 05C35
 EPrint:
 9 pages, 1 figure