Feedback Vertex Set in Mixed Graphs
Paul Bonsma, Daniel Lokshtanov

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 vertices contains a feedback vertex set (FVS) of size at most , in time . This is the first fixed parameter tractable algorithm for FVS that applies to both directed and undirected graphs.
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Taxonomy
TopicsAdvanced Graph Theory Research · Complexity and Algorithms in Graphs · Optimization and Search Problems
