Michal Karonski: Locally irregular hypergraph labelings

A weighting of the edges of a hypergraph is called locally irregular if every edge contains at least two vertices with different weighted degrees. We show that such a weighting is possible from the weight set {1,2,....,r+1} for all linear hypergraphs with maximum edge size r at least 4. The number r+1 is best possible fr this statement. Further, we prove that the r+weight set {1,2,3,4,5} is sufficient for all hypergraphs with maximum edge size 3, as well as {1,2,....5r-5} for all hypergraphs with maximum edge size r at least 4, up to some trivial exceptions.

This is a joint work with Florian Pfender and Maciej Kalkowski.