Erratum for "On oriented cliques with respect to push operation"

TL;DR

This paper corrects an earlier published theorem about minimal planar push cliques by fixing an error in the list of graphs, updating counts, and providing corrected proofs and explanations.

Contribution

It provides a corrected version of a previously published theorem, fixing the list of minimal planar push cliques and correcting related counts and proofs.

Findings

Corrected the list of 16 minimal planar push cliques

Updated counts of graphs after correction

Provided corrected proof of a key lemma

Abstract

An error is spotted in the statement of Theorem~1.3 of our published article titled "On oriented cliques with respect to push operation" (Discrete Applied Mathematics 2017). The theorem provided an exhaustive list of 16 minimal (up to spanning subgraph inclusion) underlying planar push cliques. The error was that, one of the 16 graphs from the above list was missing an arc. We correct the error and restate the corrected statement in this article. We also point out the reason for the error and comment that the error occurred due to a mistake in a particular lemma. We present the corrected proof of that particular lemma as well. Moreover, a few counts were wrongly reported due to the above mentioned error. So we update our reported counts after correction in this article.