@Article{Baudon2026,
author = "Baudon, Olivier and Bensmail, Julien and Vayssieres, Lyn",
title = "Some remarks and results on the Standard (2,2)-Conjecture",
journal = "Opuscula Math.",
year = "2026",
volume = "46",
number = "2",
pages = "127--137",
doi = "https://doi.org/10.7494/OpMath.202602101",
url = "https://doi.org/10.7494/OpMath.202602101",
abstract = "In this note, we prove that every graph can be edge-labelled with red labels \(1,2\) and blue labels \(1,2\) so that vertices with any sum of incident red labels induce a \(1\)-degenerate graph, while vertices with any sum of incident blue labels induce a \(0\)-degenerate graph. This result stands as a closer step towards the so-called Standard \((2,2)\)-Conjecture (stating that \(0\)-degeneracy can be achieved in both colours), and provides some insight on the surrounding field, which covers the 1-2-3 Conjecture, the 1-2 Conjecture, and other close problems. Along the way, we also describe how many related problems are interconnected, and raise new problems and questions for further work on the topic.",
keywords = "1-2-3 Conjecture, 1-2 Conjecture, proper labelling, labelling",
issn = "1232-9274"
}