An integer programming model for the Minimum Interval Graph Completion Problem

The minimum interval graph completion problem consists of, given a graph G=(V,E), finding a supergraph H=(V,E∪F) that is an interval graph, while adding the least number of edges |F|. We present an integer programming formulation for solving the minimum interval graph completion problem recurring to a characterization of interval graphs that produces a linear ordering of the maximal cliques of the solution graph.