Abstract:

The question of necessary and sufficient conditions for the existence of a simple hypergraph with a given degree sequence is a long-standing open problem. Let ψm(n) denote the set of all degree sequences of simple hypergraphs on vertex set [n]={1,2,⋯,n} that have m edges. A simple characterisation of ψm(n) is defined in terms of its upper and/or lower elements (degree sequences). In the process of finding all upper degree sequences, a number of results have been achieved in this paper. Classes of upper degree sequences with lowest rank (sum of degrees) rmin and with highest rank rmax have been found; in the case of rmin, the unique class of isomorphic hypergraphs has been determined; the case of rmax leads to the simple uniform hypergraph degree sequence problem. A smaller generating set has been found for ψm(n). New classes of upper degree sequences have been generated from the known sequences in dimensions less than n.

Publisher:

Elsevier

Date submitted:

31.10.2010

Date accepted:

22.07.2013

Date of publication:

30.01.2014

Identifier:

oai:noad.sci.am:136125

DOI:

10.1016/j.dam.2013.07.015

ISSN:

0166-218X

Language:

English

Journal or Publication Title:

Discrete Applied Mathematics

Volume:

163

Number:

2

URL:

Additional Information:

hasmik@ipia.sci.am

Affiliation:

Institute for Informatics and Automation Problems

Country:

Armenia

Indexing:

WOS