On the set of simple hypergraph degree sequences
Hasmik Sahakyan · Applied Mathematical Sciences · 2015
For a given m, 0 < m ≤ 2, let Dm(n) denote the set of all hypergraphic sequences for hypergraphs with n vertices and m hyperedges. A hypergraphic sequence in Dm(n) is upper hypergraphic if all its components are at least m/2. Let ��m(n) denote the set of all upper hypergraphic sequences. A structural characterization of the lowest and highest rank maximal elements of ��m(n) was provided in an earlier study. In the current paper we present an analogous characterization for all upper non-hypergraphic sequences. This allows determining the thresholds ��min and rmax such that all upper sequences of ranks lower than ��min are hypergraphic and all sequences of ranks higher than rmax are non-hypergraphic.