hClique: An exact algorithm for maximum clique problem in uniform hypergraphs
José Torres-Jiménez, Jose Carlos Perez‐Torres, Gildardo Maldonado-Martinez · Discrete Mathematics Algorithms and Applications · 2017
A hypergraph [Formula: see text] with vertex set [Formula: see text] and edge set [Formula: see text] differs from a graph in that an edge can connect more than two vertices. An r-uniform hypergraph [Formula: see text] is a hypergraph with hyperedges of size [Formula: see text]. For an r-uniform hypergraph [Formula: see text], an r-uniform clique is a subset [Formula: see text] of [Formula: see text] such as every subset of [Formula: see text] elements of [Formula: see text] belongs to [Formula: see text]. We present hClique, an exact algorithm to find a maximum r-uniform clique for [Formula: see text]-uniform graphs. In order to evidence the performance of hClique, 32 random [Formula: see text]-graphs were solved.