An upper bound on the sum of squares of degrees in a hypergraph

Authors:
Christian Bey
Affiliations:
Fakultät für Mathematik / IAG, Universitätsplatz 2, Otto-von-Guericke Universität, Magdeburg 39106, Germany
Venue:
Discrete Mathematics
Year:
2003

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Abstract

We give an upper bound on the sum of squares of l-degrees in a k-uniform hypergraph in terms of l, k and the number of vertices and edges of the hypergraph, where a l-degree is the number of edges of the hypergraph containing a fixed l-element subset of the vertices. For ordinary graphs this bound coincides with one given by de Caen. We show that our bound implies the quadratic LYM-inequality for 2-level antichains of subsets of a finite set.