For a given m, 0 < m ≤ 2 n, 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 ^Dm (n) denote the set of all upper hypergraphic sequences. A structural characterization of the lowest and highest rank maximal elements of ^Dm (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 r ̅ min and r�� such that all upper sequences of ranks lower than r ̅ min are hypergraphic and all sequences of ranks higher than r�� are non-hypergraphic.
oai:noad.sci.am:135985
Institute for Informatics and Automation Problems
Mar 2, 2021
Jul 28, 2020
20
https://noad.sci.am/publication/149598
Edition name | Date |
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Hasmik Sahakyan, On the Set of Simple Hypergraph Degree Sequences | Mar 2, 2021 |
Sahakyan Hasmik Ryazanov Vladimir Margaryan Ani
Sahakyan Hasmik Margaryan Ani
Sahakyan Hasmik Aslanyan Levon
Sahakyan Hasmik Aslanyan Levon Ryazanov Vladimir