The Turán number of a graph H is the maximum number of edges in any graph on n vertices which does not contain H as a subgraph. We call a graph Hforestable if it is cyclic, bipartite, and contains a vertex v such that \(H[V\setminus v]\) is a forest. For a forestable graph H, we determine \({\text {ex}}(n,k\cdot H)\) exactly as a function of \({\text {ex}}(n,H)\). This is related to earlier work of the authors on the Turán numbers for equibipartite forests.

中文翻译：

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禁止可植图的多个副本

图H的Turán数是n个不包含H作为子图的顶点在任何图上的最大边数。我们将图H称为可森林的，如果它是循环的，两部分的并且包含顶点v使得\（H [V \ setminus v] \）是一个森林。对于可植树图H，我们确定\（{\ text {ex}}（n，k \ cdot H）\）正是\（{\ text {ex}}（n，H）\）的函数。这与作者关于等分森林的图兰数的早期工作有关。