Log In Sign Up

Computing Subset Feedback Vertex Set via Leafage

by   Charis Papadopoulos, et al.

Chordal graphs are characterized as the intersection graphs of subtrees in a tree and such a representation is known as the tree model. Restricting the characterization results in well-known subclasses of chordal graphs such as interval graphs or split graphs. A typical example that behaves computationally different in subclasses of chordal graph is the Subset Feedback Vertex Set (SFVS) problem: given a graph G=(V,E) and a set S⊆ V, SFVS asks for a minimum set of vertices that intersects all cycles containing a vertex of S. SFVS is known to be polynomial-time solvable on interval graphs, whereas SFVS remains -complete on split graphs and, consequently, on chordal graphs. Towards a better understanding of the complexity of SFVS on subclasses of chordal graphs, we exploit structural properties of a tree model in order to cope with the hardness of SFVS. Here we consider variants of the leafage that measures the minimum number of leaves in a tree model. We show that SFVS can be solved in polynomial time for every chordal graph with bounded leafage. In particular, given a chordal graph on n vertices with leafage ℓ, we provide an algorithm for SFVS with running time n^O(ℓ). Pushing further our positive result, it is natural to consider a slight generalization of leafage, the vertex leafage, which measures the smallest number among the maximum number of leaves of all subtrees in a tree model. However, we show that it is unlikely to obtain a similar result, as we prove that SFVS remains -complete on undirected path graphs, i.e., graphs having vertex leafage at most two. Moreover, we strengthen previously-known polynomial-time algorithm for SFVS on directed path graphs that form a proper subclass of undirected path graphs and graphs of mim-width one.


page 1

page 2

page 3

page 4


Subset Feedback Vertex Set on Graphs of Bounded Independent Set Size

The (Weighted) Subset Feedback Vertex Set problem is a generalization of...

Reconfiguration of Colorable Sets in Classes of Perfect Graphs

A set of vertices in a graph is c-colorable if the subgraph induced by t...

Maximizing Communication Throughput in Tree Networks

A widely studied problem in communication networks is that of finding th...

On Some Combinatorial Problems in Cographs

The family of graphs that can be constructed from isolated vertices by d...

Length-Bounded Cuts: Proper Interval Graphs and Structural Parameters

In the presented paper we study the Length-Bounded Cut problem for speci...

Polynomial Time Algorithm for ARRIVAL on Tree-like Multigraphs

A rotor walk in a directed graph can be thought of as a deterministic ve...

The complexity of computing optimum labelings for temporal connectivity

A graph is temporally connected if there exists a strict temporal path, ...