The Leafed Induced Subtree in chordal and bounded treewidth graphs
For graph algorithm researchers, this extends tractable cases of an NP-complete problem to broader graph classes, but the results are incremental.
The paper addresses the Fully Leafed Induced Subtrees problem, providing an FPT algorithm parameterized by treewidth and a polynomial algorithm for chordal graphs, generalizing previous results for trees and series-parallel graphs.
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.