# A note on "Extremal graphs with bounded vertex bipartiteness number"

## TL;DR

This paper provides counterexamples to a previous theorem on extremal graphs with bounded vertex bipartiteness number, and offers a corrected theorem and proof to address the identified issues.

## Contribution

It identifies errors in a prior theorem, supplies counterexamples, and presents a corrected version with a valid proof.

## Key findings

- Two counterexamples disproving the original theorem
- A corrected theorem with a valid proof
- Clarification of the conditions for extremal graphs

## Abstract

This paper is devoted to present two counterexamples to the theorem from \cite{MK} Maria R., Katherine T. M., Bernardo S. M., Extremal graphs with bounded vertex bipartiteness number, Linear Algebra Appl. 493 (2016) 28-36. Moreover, the corrected theorem and proof are presented.