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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2508.13210 |
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- In this note, we revisit the notion of strong set-colorings introduced by Hegde (2009) and completed by equivalences due to Boutin et al. (2010) and provide a necessary and sufficient \emph{Steiner packing} characterisation: a finite graph $G$ is strongly set-colorable if and only if its associated $3$-uniform hypergraph is a $(2,3,2^{n}-1)$-packing of the unique Steiner triple system $S(2,3,2^{n}-1)$. This unification allows many earlier necessary conditions to be derived instantly as corollaries, streamlining the structure theory of strongly set-colorable graphs.