The Two Bicliques Problem is in NP intersection coNP

TL;DR

This paper proves that determining whether a graph's vertices can be covered with two bicliques is in NP∩coNP, suggesting it is unlikely to be NP-complete and bringing us closer to understanding its true complexity.

Contribution

The paper establishes that the two bicliques problem is in NP∩coNP, resolving a long-standing open question about its computational complexity.

Findings

The problem is in NP∩coNP.

A polynomial-time algorithm is more plausible than NP-completeness.

The result narrows the gap in understanding the problem's complexity.

Abstract

We show that the problem of deciding whether the vertex set of a graph can be covered with at most two bicliques is in NP$\cap$coNP. We thus almost determine the computational complexity of a problem whose status has remained open for quite some time. Our result implies that a polynomial time algorithm for the problem is more likely than it being NP-complete unless P = NP.