Regular graphs are antimagic
Discrete Mathematics
2019-01-10 v2 Combinatorics
Abstract
An undirected simple graph is called antimagic if there exists an injective function such that for any pair of different nodes . In a previous version of the paper, the authors gave a proof that regular graphs are antimagic. However, the proof of the main theorem is incorrect as one of the steps uses an invalid assumption. The aim of the present erratum is to fix the proof.
Cite
@article{arxiv.1504.08146,
title = {Regular graphs are antimagic},
author = {Kristóf Bérczi and Attila Bernáth and Máté Vizer},
journal= {arXiv preprint arXiv:1504.08146},
year = {2019}
}
Comments
In a previous version of the paper, the authors gave a proof that regular graphs are antimagic. However, in the proof of Claim 6, case 2 assumes that $f(e)>\ell$ for every $e\in E(v_{i-1})-E'_i$. This assumption does not hold for edges in $E^\sigma_i$, thus the subsequent calculations are incorrect. The aim of the present erratum is to fix the proof