The 1-2-3-Conjecture for Hypergraphs
Maciej Kalkowski, Michał Karoński, Florian Pfender · Journal of Graph Theory · 2016
A weighting of the edges of a hypergraph is called vertex-coloring if the weighted degrees of the vertices yield a proper coloring of the graph, i.e. every edge contains at least two vertices with different weighted degrees. In this article, we show that such a weighting is possible from the weight set for all hypergraphs with maximum edge size and not containing edges solely consisting of identical vertices. The number is best possible for this statement.