The Degree Sequence Problem for 3-Hypergraphs

Abstract

Currently the degree sequence problem for 3-hypergraphs is still unsolved efficiently. This paper researches the 3-hypergraphic problem in terms of edge switching and exchanges in the sequence to implement Dewdney’s reduction. It proposes the idea of an irreducible decomposition and makes use of it to find some sufficient conditions for a 3-hypergraphic sequence. In addition, this paper explores a related problem: intersection preserving mappings.