'Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Gora'
Publication date
01/01/1999
Field of study
A d-uniform hypergraph is a sum hypergraph iff there is a finite S β INβΊ such that is isomorphic to the hypergraph βΊdβ(S)=(V,), where V = S and =v1β,...,vdβ:(iξ =jβviβξ =vjβ)β§βi=1dβviββS. For an arbitrary d-uniform hypergraph the sum number Ο = Ο() is defined to be the minimum number of isolated vertices w1β,...,wΟββ/V such that βͺw1β,...,wΟβ is a sum hypergraph. In this paper, we prove Ο(n1β,...,ndβdβ)=1+βi=1dβ(niββ1)+min0,β1/2(βi=1dβ1β(niββ1)βndβ)β, where n1β,...,ndβdβ denotes the d-partite complete hypergraph; this generalizes the corresponding result of Hartsfield and Smyth [8] for complete bipartite graphs