Cellular telephone networks and random maps in hypergraphs Original Research Article

Let H=(V,E) be an r-uniform hypergraph of size n such that each edge of H meets at most d others. A finite map f: X→E induces a bipartite graph GH,f=(Vf,Ef) with vertex set Vf=X∪Y, where Y=⋃E, and with edge set Ef={{x,y}: x∈X, y∈f(x)}. We study matchings in the bipartite graph induced by a random f. The study was suggested by consideration of the call sequence acceptance behavior of a load-sharing system for cellular telephone networks, invented by Matula and Yang.