A disconnected cut of a connected graph is a vertex cut that itself also induces a disconnected subgraph. The corresponding decision problem is called Disconnected Cut. This problem is known to be NP-hard on general graphs. We prove that it is polynomial-time solvable on claw-free graphs, answering a question of Ito et al. (TCS 2011). The basis for our result is a decomposition theorem for claw-free graphs of diameter 2, which we believe is of independent interest and builds on the research line initiated by Chudnovsky and Seymour (JCTB 2007–2012) and Hermelin et al. (ICALP 2011). On our way to exploit this decomposition theorem, we characterize how disconnected cuts interact with certain cobipartite subgraphs, and prove two further algorithmic results, namely that Disconnected Cut is polynomial-time solvable on circular-arc graphs and line graphs.

连接图的不连续切割是一个顶点切割，它本身也可以引发不连续的子图。相应的决策问题称为Disconnected Cut。已知此问题在一般图形上是NP难的。我们证明了它在无爪图中是多项式时间可解的，回答了伊藤等人的问题。（TCS 2011）。我们的结果的基础是直径为2的无爪图的分解定理，我们认为这是独立的兴趣，它建立在Chudnovsky和Seymour（JCTB 2007–2012）和Hermelin等人的研究基础上。（ICALP 2011）。在利用这一分解定理的方法中，我们表征了不连续的割线如何与某些共邻子图相互作用，并证明了另外两个算法结果，即Disconnected Cut在圆弧图和线图上可以多项式求解。