On the set of simple hypergraph degree sequences

Hasmik Sahakyan
2015 Applied Mathematical Sciences  
For a given , 0 < ≤ 2 , let ( ) denote the set of all hypergraphic sequences for hypergraphs with vertices and hyperedges. A hypergraphic sequence in ( ) is upper hypergraphic if all its components are at least /2. Let ̂( ) denote the set of all upper hypergraphic sequences. A structural characterization of the lowest and highest rank maximal elements of ̂( ) was provided in an earlier study. In the current paper we present an analogous characterization for all upper non-hypergraphic sequences.
more » ... This allows determining the thresholds ̅ and such that all upper sequences of ranks lower than ̅ are hypergraphic and all sequences of ranks higher than are non-hypergraphic.
doi:10.12988/ams.2015.411972 fatcat:e4zjrz5nl5dcrkhqulax4yjwsm