On mod sum hypergraphs

Abstract

A hypergraph ℋ is a mod sum hypergraph iff there exists a positive m, a finite S ⊂ {1, 2,... ,m - 1} and d_min,d_max ∈ N⁺ with 1 < d_min ≤ d_max such that ℋ is isomorphic to the hypergraph ℋ_min,d_max(S) - (V,ℰ) where V = S and (Equation Presented). Note that sum hypergraphs as defined by Martin Sonntag, Hanns-Martin Teichert are mod sum hypergraphs, but the converse is not true. In this paper, we show that for d ≥ 3 d-uniform hypertrees and d-uniform hypercycles are mod sum hypergraphs. Moreover, we prove that d-uniform complete hypergraph are mod sum hypergraphs if d = n,n - 1, d-uniform complete hypergraph are not mod sum hypergraphs if n ≥ 2 ^d + d.