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：在完全带叶诱导子树问题中，给定一个图$G$以及两个整数$a$和$b$，目标是寻找$G$的一个包含$a$个顶点且至少具有$b$个叶子的诱导子树。已知即使输入图是$4$-正则图，该问题也是NP完全的。当输入图限制为树或串并联图时，存在多项式时间算法。本文通过给出一个以树宽为参数的FPT算法，推广了上述结果。同时，当输入图限制为弦图时，我们提供了一个多项式时间算法。