TY  - JOUR
ID  - Baudon2026
LB  - Baudon2026
AU  - Baudon, Olivier
AU  - Bensmail, Julien
AU  - Vayssieres, Lyn
TI  - Some remarks and results on the Standard (2,2)-Conjecture
ST  - Some remarks and results on the Standard (2,2)-Conjecture
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2026
VL  - 46
IS  - 2
SP  - 127
EP  - 137
DO  - https://doi.org/10.7494/OpMath.202602101
UR  - https://doi.org/10.7494/OpMath.202602101
AB  - 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.
KW  - 1-2-3 Conjecture
KW  - 1-2 Conjecture
KW  - proper labelling
KW  - labelling
SN  - 1232-9274
ER  -