A 9/4-Approximation for Directed Feedback Vertex Sets in Quasi-Transitive Digraphs

A $2$-Approximation for Directed Feedback Vertex Set in Locally Semicomplete and Quasi-Transitive Digraphs

This work achieves the first non-trivial constant-factor approximation for \textsc{DFVS} on \textsf{LSD}s, even in the unweighted setting, and improves the recent deterministic $9/4$-approximation of Ghorbani and Mnich~[ICALP'26].

A BRANCH AND BOUND ALGORITHM FOR FINDING THE POSITIVE INFLUENCE DOMINATING SET ON CHORDAL GRAPHS

This paper develops an exact algorithm based on the Branch and Bound approach for solving PIDS on chordal graphs, which involves identifying the smallest group of vertices in a given network that maximizes influence throughout the network.

A Polynomial Kernel for Planar Directed Feedback Vertex Set

The Directed Feedback Vertex Set problem (DFVS) asks whether a digraph can be made acyclic by deleting at most $k$ vertices. Whether DFVS admits a polynomial kernel parameterized by $k$ is a major open problem in kernelization, even for planar digraphs. We resolve the planar case by giving a deterministic kernel with $...

Exponential Lower Bounds for Integer-Weighted Shortest-Paths Preservers of DAGs

It is proved that there exist DAGs for which any shortest-paths preserving integer reweighting requires weights of size $2^{\Omega(n)}$, even when the DAG has very simple structure.

Perfect Italian Domination on Structured Bipartite Graphs: Algorithms, Parameterization, and Hardness

It is proved that the decision problem is NP-complete on star-convex bipartite graphs and the problem parameterized by the target weight is W[1]-hard on the same graph class through a parameter-preserving reduction from Perfect Code.

Upper Clique Transversal on Interval Graphs and Beyond