论文标题
HyperCube中的广义Turán密度
Generalized Turán densities in the hypercube
论文作者
论文摘要
经典的极端或Turán类型问题要求确定$ {\ rm ex}（g，h）$，这是图$ g $的子图中最大数量的边缘，该边缘不包含$ h $的子量度同构。 Alon和Shikhelman引入了所谓的广义极值$ {\ rm ex}（g，t，h）$，定义为最大$ g $中的$ t $的亚毛学同构的最大数量，其中包含$ g $，其中不包含子级别的子级别等差异至$ h $。在本文中，我们调查了$ g = q_n $，尺寸$ n $，$ t $和$ h $的案例，是较小的超级立管或周期。
A classical extremal, or Turán-type problem asks to determine ${\rm ex}(G, H)$, the largest number of edges in a subgraph of a graph $G$ which does not contain a subgraph isomorphic to $H$. Alon and Shikhelman introduced the so-called generalized extremal number ${\rm ex}(G,T,H)$, defined to be the maximum number of subgraphs isomorphic to $T$ in a subgraph of $G$ that contains no subgraphs isomorphic to $H$. In this paper we investigate the case when $G = Q_n$, the hypercube of dimension $n$, and $T$ and $H$ are smaller hypercubes or cycles.
