论文标题
随机Turán问题的随机多项式图
Random Polynomial Graphs for Random Turán Problems
论文作者
论文摘要
Bukh和Conlon使用随机多项式图在$ \ mathrm {ex}（n，\ Mathcal {t}^\ ell）$上提供有效的下限，其中$ \ Mathcal {t}^\ ell $是$ \ ell $ \ ell $ th balanced lot $ th balanced looted looted looted树的功率。我们扩展了它们的结果，以在$ \ mathrm {ex}（g_ {n，p}，\ mathcal {t}^\ ell）$上提供有效的下限，这是$ \ nathcal {t}^\ ell $ - free $ g_ g_ g_ g_ g_ {也证明了随机图中广义Turán数字的类似边界。
Bukh and Conlon used random polynomial graphs to give effective lower bounds on $\mathrm{ex}(n,\mathcal{T}^\ell)$, where $\mathcal{T}^\ell$ is the $\ell$th power of a balanced rooted tree $T$. We extend their result to give effective lower bounds on $\mathrm{ex}(G_{n,p},\mathcal{T}^\ell)$, which is the maximum number of edges in a $\mathcal{T}^\ell$-free subgraph of the random graph $G_{n,p}$. Analogous bounds for generalized Turán numbers in random graphs are also proven.
