Feedback vertex set on chordal bipartite graphs

TL;DR

This paper proves that the feedback vertex set problem, which involves finding a minimal set of vertices to break all cycles in a graph, can be efficiently solved in polynomial time specifically for chordal bipartite graphs.

Contribution

The paper establishes the polynomial-time solvability of the feedback vertex set problem on chordal bipartite graphs, a class of graphs where no induced cycles longer than four exist.

Findings

Feedback vertex set problem is polynomial-time solvable on chordal bipartite graphs.

Chordal bipartite graphs exclude induced cycles longer than four.

Efficient algorithms are provided for this class of graphs.

Abstract

Let G=(A,B,E) be a bipartite graph with color classes A and B. The graph G is chordal bipartite if G has no induced cycle of length more than four. Let G=(V,E) be a graph. A feedback vertex set F is a set of vertices F subset V such that G-F is a forest. The feedback vertex set problem asks for a feedback vertex set of minimal cardinality. We show that the feedback vertex set problem can be solved in polynomial time on chordal bipartite graphs.