A $P_4$ is a chordless path on four vertices. A diamond is a graph obtained from a clique of size four by removing one edge of the clique. A paw is a graph obtained from a clique of size four by removing two adjacent edges of the clique. We prove that for a graph $H$, the class of graphs with no induced subdivision of $H$ has bounded clique-width if and only if $H$ is an induced subgraph of $P_4$, the paw, or the diamond. This answers a~question of Dabrowski, Johnson, and Paulusma.

翻译：$P_4$ 是顶点数为四的无弦路径。菱形图是由大小为四的团删除一条边得到的图。爪形图是由大小为四的团删除两条相邻边得到的图。我们证明：对于图 $H$，不含 $H$ 的导出细分图的图类具有有界团宽度当且仅当 $H$ 是 $P_4$、爪形图或菱形图的导出子图。这回答了 Dabrowski、Johnson 和 Paulusma 提出的一个问题。