On existence of hypergraphs with prescribed edge degree profile

Abstract

The degree profile of an edge e of a finite hypergraph H is the map assigning to a positive integer i the number of vertices of degree i incident with e. The edge degree profile of H is the map describing for any possible degree profile α the number of edges in H with degree profile α. A necessary and sufficient condition for existence of hypergraphs of prescribed edge degree profile is found. A similar result concerning hypergraphs without multiple edges is also presented. © 1995.