论文标题
与对称生长的图形的粗略分辨率
Coarse distinguishability of graphs with symmetric growth
论文作者
论文摘要
令$ x $为具有对称增长的本地连接，有限的图。我们证明，有一个顶点着色$ ϕ \ colon x \ to \ {0,1 \} $，在\ mathbb {n} $中有一些$ r \ in \ mathbb {n} $，使每个自动形态$ f $保留$ f $ cop $ f $ nistage $ ϕ $ is $ r $ close is $ r $ close close is $ r $ close to Identity Map to Indentity Map;这可以看作是对称破坏的粗几何版本。我们还证明，对于至少一个顶点稳定器$ s_x $满足以下条件的图形，无限运动猜想是正确的：对于S_X $中的每个非身份自动形态$ f \ f \ f \ f \ s_x $，都有一个序列$ x_n $，因此$ \ lim d（x_n，f（x_n）= x_n，f（x_n）= \ infty $。
Let $X$ be a connected, locally finite graph with symmetric growth. We prove that there is a vertex coloring $ϕ\colon X\to\{0,1\}$ and some $R\in\mathbb{N}$ such that every automorphism $f$ preserving $ϕ$ is $R$-close to the identity map; this can be seen as a coarse geometric version of symmetry breaking. We also prove that the infinite motion conjecture is true for graphs where at least one vertex stabilizer $S_x$ satisfies the following condition: for every non-identity automorphism $f\in S_x$, there is a sequence $x_n$ such that $\lim d(x_n,f(x_n))=\infty$.
