Correction to “A 2-regular graph has a prime labeling if and only if it has at most one odd component” [<i>Journal of Combinatorics</i> 12 (2021) 379–388]

After publication of $\href{ https://dx.doi.org/10.4310/JOC.2021.v12.n3.a1}{\textrm{the research article named above}}$, the author discovered an error in the algorithm used to prove both Theorem 2.1 (cited from another paper by the current author) and Theorem 3.5. This error has a major impact on the stated results of the original paper. This erratum explains the error and details the current status of the conjecture that a $2$–regular graph has a prime labeling if and only if it has at most one odd component.

Keywords

prime labeling, regular graph, graph labeling

2010 Mathematics Subject Classification

05C78

Full Text (PDF format)

The author would like to thank Sanjay Patel for his careful reading of the original article and for bringing this error to his attention.

Received 30 July 2022

Accepted 14 September 2022

Published 7 November 2023