In the Fully Leafed Induced Subtrees, one is given a graph $G$ and two integers $a$ and $b$ and the question is to find an induced subtree of $G$ with $a$ vertices and at least $b$ leaves. This problem is known to be NP-complete even when the input graph is $4$-regular. Polynomial algorithms are known when the input graph is restricted to be a tree or series-parallel. In this paper we generalize these results by providing an FPT algorithm parameterized by treewidth. We also provide a polynomial algorithm when the input graph is restricted to be a chordal graph.

翻译：在完全叶诱导子树问题中，给定图$G$以及两个整数$a$和$b$，需要找出$G$中具有$a$个顶点且至少包含$b$个叶子的诱导子树。已知该问题在输入图为$4$-正则图时是NP完全的。当输入图限制为树或串联并联图时，存在多项式算法。本文通过提出一个以树宽为参数的FPT算法来推广这些结果。此外，我们还给出当输入图限制为弦图时的多项式算法。