Feedback Vertex Set in Mixed Graphs

TL;DR

This paper introduces the first fixed parameter tractable algorithm for the Feedback Vertex Set problem applicable to mixed graphs containing both directed and undirected edges, with a runtime exponential in the parameter k.

Contribution

It presents a novel fixed parameter algorithm for FVS in mixed graphs, combining directed and undirected cases in a single efficient approach.

Findings

Algorithm runs in 2^{O(k)}k! O(n^4) time

First FPT algorithm for FVS in mixed graphs

Applicable to graphs with both directed and undirected edges

Abstract

A mixed graph is a graph with both directed and undirected edges. We present an algorithm for deciding whether a given mixed graph on $n$ vertices contains a feedback vertex set (FVS) of size at most $k$, in time $2^{O(k)}k! O(n^4)$. This is the first fixed parameter tractable algorithm for FVS that applies to both directed and undirected graphs.