The interplay of minimum degree conditions and structural properties of large graphs with forbidden subgraphs is a central topic in extremal graph theory. For a given graph F we define the homomorphism threshold as the infimum over all α ∈ [0,1] such that every n -vertex F -free graph G with minimum degree at least αn has a homomorphic image H of bounded order (i.e. independent of n ), which is F -free as well. Without the restriction of H being F -free we recover the definition of the chromatic threshold, which was determined for every graph F by Allen et al. [1]. The homomorphism threshold is less understood and we address the problem for odd cycles.

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奇数周期的同态阈值 Oliver Ebsen, Mathias Schacht

具有禁止子图的大图的最小度条件和结构特性的相互作用是极值图论的中心话题。对于给定的图 F，我们将同态阈值定义为所有 α ∈ [0,1] 上的下界，使得每个具有最小度数至少为 αn 的 n 顶点 F 自由图 G 具有有界阶的同态图像 H（即独立的 n )，它也是无 F 的。没有 H 是 F-free 的限制，我们恢复了色度阈值的定义，这是由 Allen 等人为每个图 F 确定的。[1]。同态阈值不太了解，我们解决了奇数周期的问题。