The 1‐2‐3‐Conjecture for Hypergraphs

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 { 1 , 2 , … , max { 5 , r + 1 } } for all hypergraphs with maximum edge size r ≥ 3 and not containing edges solely consisting of identical vertices. The number r + 1 is best possible for this statement.