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- W3034202634 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." @default.
- W3034202634 created "2020-06-19" @default.
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- W3034202634 date "2020-11-19" @default.
- W3034202634 modified "2023-10-17" @default.
- W3034202634 title "Generalizations of the Ruzsa–Szemerédi and rainbow Turán problems for cliques" @default.
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- W3034202634 doi "https://doi.org/10.1017/s0963548320000589" @default.
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