Hitting all Maximal Independent Sets of a Bipartite Graph

TL;DR

This paper proves that determining whether a size-k vertex subset hits all maximal independent sets in a bipartite graph is a computationally complex problem classified as Sigma_2^P-complete.

Contribution

It establishes the complexity classification of the hitting set problem for all maximal independent sets in bipartite graphs.

Findings

The problem is Sigma_2^P-complete.

Complexity classification for hitting all maximal independent sets.

Implications for computational complexity in graph theory.

Abstract

We prove that given a bipartite graph G with vertex set V and an integer k, deciding whether there exists a subset of V of size k hitting all maximal independent sets of G is complete for the class Sigma_2^P.