论文标题
Ruzsa-Szemerédi和RainbowTurán问题的概括
Generalizations of the Ruzsa-Szemerédi and rainbow Turán problems for cliques
论文作者
论文摘要
考虑到Ruzsa-szemerédi问题的自然概括，我们证明，对于任何固定的正整数$ r，s $带有$ r <s $的s $，在$ n $ dertices上包含$ n^{r} e^{r} e^{ - o（\ sqrt { $ k_r $最多包含一个$ k_s $。当$ f $完成时，我们还为广义的彩虹图Turán问题$ \ permatatorname {ex}（n，h，$ rainbow- $ f）$。特别是，我们回答了Gerbner，Mészáros，Methuku和Palmer的问题，表明$ N $ Vertices上有适当的边缘色图，上面有$ n^{r-1-o（1）} $ $ k_r $的副本，因此没有$ k_r $是彩虹。
Considering a natural generalization of the Ruzsa-Szemerédi 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 Turán problem $\operatorname{ex}(n, H,$rainbow-$F)$ when $F$ is complete. In particular, we answer a question of Gerbner, Mészáros, 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.
