论文标题
翻转过程的突出示例
Prominent examples of flip processes
论文作者
论文摘要
Flip processes, introduced in [Garbe, Hladký, Šileikis, Skerman: From flip processes to dynamical systems on graphons], are a class of random graph processes defined using a rule which is just a function $\mathcal{R}:\mathcal{H}_k\rightarrow \mathcal{H}_k$ from all labelled graphs of a fixed order $k$进入自己。该过程以任意给定的$ n $ vertex图$ g_0 $开始。在每个步骤中，图$ g_i $都是通过抽样$ k $随机顶点$ v_1，\ ldots，v_k $ of $ g_ {i-1} $获得的，并替换了诱导的图$ g_ {i-1} [v_1，\ ldots，\ ldots，v_k] $ by v_k] $ by $ \ Mathcal {r}（g_ {i-1} [v_1，\ ldots，v_k]）$。 使用同上与每个此类翻转过程相关的图形子上的动力学系统的形式主义。我们研究了几个特定的翻转过程，包括三角拆卸翻转过程及其概括，“极端主义翻转过程”（其中$ \ nathcal {r}（h）$是一个集团或独立集，具体取决于$ e（h）$，取决于所有潜在的$ $ $ $ $ $ $ $ n n the Intperte $ \ n n the Intupte $ \ n n the Intupter $ \ ber的一半或多个。 $ h $。
Flip processes, introduced in [Garbe, Hladký, Šileikis, Skerman: From flip processes to dynamical systems on graphons], are a class of random graph processes defined using a rule which is just a function $\mathcal{R}:\mathcal{H}_k\rightarrow \mathcal{H}_k$ from all labelled graphs of a fixed order $k$ into itself. The process starts with an arbitrary given $n$-vertex graph $G_0$. In each step, the graph $G_i$ is obtained by sampling $k$ random vertices $v_1,\ldots,v_k$ of $G_{i-1}$ and replacing the induced graph $G_{i-1}[v_1,\ldots,v_k]$ by $\mathcal{R}(G_{i-1}[v_1,\ldots,v_k])$. Using the formalism of dynamical systems on graphons associated to each such flip process from ibid. we study several specific flip processes, including the triangle removal flip process and its generalizations, 'extremist flip processes' (in which $\mathcal{R}(H)$ is either a clique or an independent set, depending on whether $e(H)$ has less or more than half of all potential edges), and 'ignorant flip processes' in which the output $\mathcal{R}(H)$ does not depend on $H$.
