Flip graphs of combinatorial and geometric objects are at the heart of many deep structural insights and connections between different branches of discrete mathematics and computer science. They also provide a natural framework for the study of reconfiguration problems. We study flip graphs of arrangements of pseudolines and of arrangements of pseudocircles, which are combinatorial generalizations of lines and circles, respectively. In both cases we consider triangle flips as local transformation and prove conjectures regarding their connectivity. In the case of $n$ pseudolines we show that the connectivity of the flip graph equals its minimum degree, which is exactly $n-2$. For the proof we introduce the class of shellable line arrangements, which serve as reference objects for the construction of disjoint paths. In fact, shellable arrangements are elements of a flip graph of line arrangements which are vertices of a polytope (Felsner and Ziegler; DM 241 (2001), 301--312). This polytope forms a cluster of good connectivity in the flip graph of pseudolines. In the case of pseudocircles we show that triangle flips induce a connected flip graph on \emph{intersecting} arrangements and also on cylindrical intersecting arrangements. The result for cylindrical arrangements is used in the proof for intersecting arrangements. We also show that in both settings the diameter of the flip graph is in $\Theta(n^3)$. Our constructions make essential use of variants of the sweeping lemma for pseudocircle arrangements (Snoeyink and Hershberger; Proc.\ SoCG 1989: 354--363). We finally study cylindrical arrangements in their own right and provide new combinatorial characterizations of this class.

翻译：组合与几何对象的翻转图是离散数学与计算机科学各分支间深层结构洞察及关联的核心，也为重构问题的研究提供了自然框架。本文研究伪直线排列与伪圆排列的翻转图——这两类对象分别对应直线与圆的组合推广。我们针对三角形翻转这类局部变换，分别证明了关于其连通性的猜想。对于$n$条伪直线的情形，我们证明翻转图的连通度等于其最小度$n-2$。证明中引入可壳线性排列类，作为构造不相交路径的参考对象。事实上，可壳排列是线排列翻转图中的元素，这些元素构成某个多面体的顶点（Felsner和Ziegler; DM 241 (2001), 301–312）。该多面体在伪直线翻转图中形成高连通性簇。对于伪圆情形，我们证明三角形翻转在{相交}排列及其圆柱形相交排列上均诱导出连通翻转图。圆柱形排列的结论被用于相交排列的证明。我们还证明两种情形下翻转图的直径均为$\Theta(n^3)$。我们的构造本质地使用了伪圆排列扫描引理的变体（Snoeyink和Hershberger; Proc.\ SoCG 1989: 354–363）。最后，我们独立研究圆柱形排列，并给出该类别的新组合刻画。