# About a counterexample on contractible transformations of graphs

## TL;DR

This paper critically examines Ivashchenko's claims about contractible transformations of graphs, providing a counterexample that invalidates his previous results and highlighting errors in his proofs.

## Contribution

The paper presents a counterexample demonstrating that Ivashchenko's earlier results on contractible transformations are incorrect, correcting the understanding of graph homology invariance.

## Key findings

- Counterexample disproves Ivashchenko's claims
- Identifies errors in previous proofs
- Clarifies the limitations of contractible transformations

## Abstract

In [A. V. Ivashchenko, Contractible transformations do not change the homology groups of graphs, Discrete Mathematics 126 (1) (1994) p 159,170], Ivashchenko started with the study of contractible graphs, he began with this because they have application to molecular spaces. But in a second paper [A. V. Ivashchenko, Some properties of contractible transformations on graphs, Discrete Mathematics 133 (1) (1994) p 139,145], he made several mistakes. We show in this paper that the results in that second paper are false or the proofs are wrong.