论文标题
（准）中值图的交叉和接触图中的翻译长度
Translation lengths in crossing and contact graphs of (quasi-)median graphs
论文作者
论文摘要
鉴于准米迪安图$ x $，交叉图$ΔX$和触点图$γx$是$ x $的天然双曲线型号。在本文中，我们表明，$ x $的等轴测图中的渐近翻译长度始终是理性的。此外，如果$ x $是双曲线的，那么这些理性数字可以用统一界面的分母编写；在整个普遍性中并非如此。最后，我们表明，如果从某种意义上说，如果Quasi-Median Graph $ x $可以构造，那么就存在一个算法计算每个可计算等轴测的翻译长度。我们的结果涵盖了CAT（0）立方体复合物中的触点图和右角Artin组的扩展图。
Given a quasi-median graph $X$, the crossing graph $ΔX$ and the contact graph $ΓX$ are natural hyperbolic models of $X$. In this article, we show that the asymptotic translation length in $ΔX$ or $ΓX$ of an isometry of $X$ is always rational. Moreover, if $X$ is hyperbolic, these rational numbers can be written with denominators bounded above uniformly; this is not true in full generality. Finally, we show that, if the quasi-median graph $X$ is constructible in some sense, then there exists an algorithm computing the translation length of every computable isometry. Our results encompass contact graphs in CAT(0) cube complexes and extension graphs of right-angled Artin groups.
