4-Hyperclique Decompositions of 3-Hyperdistance Multihypergraphs of Multipartite Graphs: Chutima Saengchampa, Chariya Uiyyasathian - Team, Support (Thai Journal of Mathematics, 2021)
This paper investigates hyperclique decompositions of a hypergraph transformation, namely the hyperdistance multihypergraph defined as follows: Given an integer k≥ 3 and any hypergraph H, the k-hyperdistance multihypergraph of H, denoted by D^(k)(H), is the k-uniform hypergraph which has the same vertex set as H and for any k-subset {v_1, v_2, … v_k} of V(H), D^(k)(H) has exactly _i eq j^ d_H(v_i, v_j) copies of hyperedges {v_1, v_2, …, v_k} where d_H(v_i, v_j) is the distance between vertices v_i and v_j in H. We study 4-hyperclique decompositions of D^(3)(H) where H is a complete multipartite graph. Our construction technique includes classic designs such as Latin cubes and factorizations of graphs.