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Many $H$-copies in graphs with a forbidden tree
- Publication Year :
- 2018
-
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 well-studied Tur\'an 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.<br />Comment: 9 pages, 1 figure
- Subjects :
- Mathematics - Combinatorics
05C35
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1811.04287
- Document Type :
- Working Paper