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Generalizations of the Ruzsa-Szemer'edi and rainbow Tur'an problems for cliques | | W. T. Gowers
; Barnabás Janzer
; | | Date: |
5 Mar 2020 | | Abstract: | Considering a natural generalization of the Ruzsa-Szemer’edi problem, we
prove that for any fixed positive integers $r,s$ with $r<s$, there are graphs
on $n$ vertices containing $n^{r}e^{-O(sqrt{log{n}})}=n^{r-o(1)}$ copies of
$K_s$ such that any $K_r$ is contained in at most one $K_s$. We also give
bounds for the generalized rainbow Tur’an problem $operatorname{ex}(n,
H,$rainbow-$F)$ when $F$ is complete. In particular, we answer a question of
Gerbner, M’esz’aros, Methuku and Palmer, showing that there are properly
edge-coloured graphs on $n$ vertices with $n^{r-1-o(1)}$ copies of $K_r$ such
that no $K_r$ is rainbow. | | Source: | arXiv, 2003.2754 | | Services: | Forum | Review | PDF | Favorites | |
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