The hypergraph 1-2-3 Conjecture
The hypergraph 1-2-3 Conjecture
Let be a hypergraph whose edges have orders between and , with no edge consisting of twins. A weighting induces vertex weights
Hypergraph 1-2-3 Conjecture. There is such a weighting for which the induced vertex weights properly color .
The conjecture proposes that the bound proved for linear hypergraphs extends to all hypergraphs under the stated exclusion of edges consisting of twins. The source gives no resolution status.
Sources & referencesView supporting material
Primary source
Maciej Kalkowski, Michał Karoński and Florian Pfender, “The 1-2-3 Conjecture for Hypergraphs”, arXiv:1308.0611 (2016).
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