The weak 3-weighting conjecture for uniform hypergraphs
The weak 3-weighting conjecture for uniform hypergraphs
Let be an -uniform hypergraph without isolated edges, where . A weight function is a map , inducing the vertex-coloring by
The coloring is weak if no edge is monochromatic, and is weakly 3-weighted if some such weight function induces a weak coloring.
Weak 3-weighting conjecture. For each , every -uniform hypergraph without isolated edges is weakly 3-weighted.
This extends the graph 1-2-3 conjecture to uniform hypergraphs and strengthens the previously mentioned weak weighting results. The claim is presented as an open belief in the source, with no resolution supplied.
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Sources & referencesView supporting material
Primary source
Patrick Bennett, Andrzej Dudek, Alan Frieze and Laars Helenius, “Weak and strong versions of the 1-2-3 conjecture for uniform hypergraphs”, arXiv:1511.04569 (2015).
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