The 1‐2‐3‐Conjecture for Hypergraphs |
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| Authors: | Maciej Kalkowski Micha? Karoński Florian Pfender |
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| Institution: | 1. FACULTY OF MATHEMATICS AND COMPUTER SCIENCE, ADAM MICKIEWICZ UNIVERSITY, POZNA?, POLAND;2. DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE, EMORY UNIVERSITY, ATLANTA, GA;3. DEPARTMENT OF MATHEMATICAL AND STATISTICAL SCIENCES, UNIVERSITY OF COLORADO DENVER, DENVER, CO |
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| Abstract: | 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. |
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| Keywords: | irregular hypergraph labelings 05C78 (05C15) |
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for all hypergraphs with maximum edge size 
and not containing edges solely consisting of identical vertices. The number 
is best possible for this statement.