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The 1‐2‐3‐Conjecture for Hypergraphs
Authors:Maciej Kalkowski  Micha? Karoński  Florian Pfender
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
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 urn:x-wiley:03649024:media:jgt22100:jgt22100-math-0001 for all hypergraphs with maximum edge size urn:x-wiley:03649024:media:jgt22100:jgt22100-math-0002 and not containing edges solely consisting of identical vertices. The number urn:x-wiley:03649024:media:jgt22100:jgt22100-math-0003 is best possible for this statement.
Keywords:irregular hypergraph labelings  05C78  (05C15)
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